Tổng của hàng thứ 3 trong tam giác pascal là bao nhiêu?
Tam giác Pascal là một mảng số đại diện cho một mẫu số. Nó có một số cách sử dụng khác nhau trong toán học và thống kê, nhưng trong ngữ cảnh của đa thức, cụ thể là nhị thức, nó được sử dụng để mở rộng các nhị thức Show Tính chất của tam giác PascalDưới đây là một phần của tam giác Pascal;
Có những tính chất khác của tam giác Pascal ngoài những tính chất được liệt kê ở trên, nhưng việc hiểu những tính chất được liệt kê ở trên có thể hữu ích khi sử dụng tam giác Pascal để mở rộng các nhị thức khai triển nhị thứcCó thể sử dụng tam giác Pascal để xác định các hệ số khi khai triển nhị thức. Cụ thể, hệ số nhị thức, thường được viết là , cho chúng ta biết mục thứ b của hàng thứ n của tam giác Pascal; . Ví dụ Mở rộng. (x + y)3 Tham khảo hình sau cùng với lời giải thích bên dưới Trong ví dụ này, n = 3, biểu thị hàng thứ 4 của tam giác Pascal (vì hàng đầu tiên là n = 0). Các số trong hàng, 1 3 3 1, là các hệ số và b cho biết chúng ta đang đề cập đến hệ số nào trong hàng. Tham khảo lại ví dụ trên. Hệ số của số hạng đầu tiên, x3, là ở b = 0 của hàng n = 3, hoặc 1. Tương tự cho mỗi số hạng tương ứng sao cho hệ số của các số hạng thứ 2, 3 và 4 lần lượt là 3, 3 và 1, đúng như ở hàng n = 3 của tam giác Pascal Tiếp theo, chúng ta có thể xác định giá trị của các biểu thức nhân với từng hệ số. Mỗi số hạng có một số thành phần của x và một số thành phần của y được nâng lên thành số mũ. Số mũ trên các thành phần x và y có tổng bằng n. Bắt đầu từ bên trái, x có số mũ bằng n hoặc 3 và y có số mũ bằng 0. Di chuyển từ trái sang phải, 1 bị trừ khỏi số mũ trên thành phần x trong khi 1 được thêm vào số mũ trên thành phần y, dẫn đến số hạng cuối cùng có số mũ là 0 trên thành phần x và số mũ là 3 trên thành phần x. . Điều này có thể được nhìn thấy trong ví dụ trên, trong đó các số mũ trên mỗi thuật ngữ được viết rõ ràng Sử dụng tam giác Pascal và các mẫu này, chúng ta có thể mở rộng các nhị thức được nâng lên lũy thừa bậc n mà nếu không sẽ rất tẻ nhạt để mở rộng thông qua phép nhân lặp đi lặp lại. Tham khảo trang định lý nhị thức để biết cách tiếp cận công thức để khai triển các nhị thức, cách này thậm chí còn hiệu quả hơn khi bạn đã quen thuộc với tất cả các ký hiệu toán học trong công thức Cách tiếp cận ngây thơ. Trong tam giác Pascal, mỗi mục của một hàng là giá trị của hệ số nhị thức. Vì vậy, một giải pháp đơn giản là tạo tất cả các phần tử hàng cho đến hàng thứ n và thêm chúng. Nhưng cách tiếp cận này sẽ có độ phức tạp thời gian O(n3). Tuy nhiên, nó có thể được tối ưu hóa lên đến độ phức tạp thời gian O(n2). Tham khảo bài viết sau để tạo các phần tử của tam giác Pascal.
Giải pháp tốt hơn. Cùng tìm hiểu về mẫu tam giác của pascal sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 210 Như hình trên tổng các phần tử ở hàng thứ i bằng 2i. Giờ đây, có thể dễ dàng tính tổng của tất cả các phần tử cho đến hàng thứ n bằng cách cộng các lũy thừa của 2 Dưới đây là việc thực hiện phương pháp trên. C++
Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 10
Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 11 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 12 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 13 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 13 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 15 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 16 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 15 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 18 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 19
sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2101 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 13 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 13 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 15 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2106
sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2108 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Sum of all elements:10230 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Sum of all elements:10232 Sum of all elements:10233 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 15 Sum of all elements:10235 Sum of all elements:10236_______21_______7 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Sum of all elements:10239
sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Sum of all elements:10231 Sum of all elements:10232 Sum of all elements:10239
Sum of all elements:10234 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 15 Sum of all elements:10236 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 19 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 15 // C++ program to find sum of all elements 0sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 // C++ program to find sum of all elements 2// C++ program to find sum of all elements 3 // C++ program to find sum of all elements 4sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Sum of all elements:10231 // C++ program to find sum of all elements 7Sum of all elements:10239 Java
sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 11 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 12 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 #include 0 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 13 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 16 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 15 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 18 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 19
Sum of all elements:10236 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2101 Sum of all elements:10236_______1_______3 using 1using 2using 3
Sum of all elements:10236_______0_______8 Sum of all elements:10236_______21_______0 Sum of all elements:10236_______21_______2 Sum of all elements:10233 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 15 namespace 2using 2namespace 4
Sum of all elements:10236_______21_______9
Sum of all elements:10236_______21_______1 Sum of all elements:10232 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Sum of all elements:10239
sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 107 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 109 #include 0 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 111 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 112 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 19 Sum of all elements:10236_______1_______5 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 117_______1_______18 using 3Sum of all elements:10236_______1_______21 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 122 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 123 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 124 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Sum of all elements:10239 Sum of all elements:10239 Python3Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 128 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 129
Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 130 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 131 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 132 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 133 Sum of all elements:10236 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 136 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 138 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 139 using 2sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 143 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 145 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Sum of all elements:10232 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 148 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 149 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 150 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 151 Sum of all elements:10236_______1_______38 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 139 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 138 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 156 Sum of all elements:10233 namespace 7 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 159
sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Sum of all elements:10231 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 138 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 164 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 165 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 139 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 118 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 168 Sum of all elements:10233 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 122 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 171 C#Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 172
Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 175
Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 109 // upto nth row in Pascal triangle. 3 // upto nth row in Pascal triangle. 4
sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 11 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 12 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 #include 0 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 13 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 16 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 15 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 18 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 19
Sum of all elements:10236 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2101 Sum of all elements:10236_______1_______3 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2106
Sum of all elements:10236_______0_______8 Sum of all elements:10236_______21_______0 Sum of all elements:10236_______21_______2 Sum of all elements:10233 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 15 Sum of all elements:10235
Sum of all elements:10237 Sum of all elements:10236_______21_______9
Sum of all elements:10236_______21_______1 Sum of all elements:10232 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Sum of all elements:10239
sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 #include 0 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 109 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 111 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21018 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 19 Sum of all elements:10236_______1_______5 // C++ program to find sum of all elements 0Sum of all elements:10236_______0_______25 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 122 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21027______1_______24 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Sum of all elements:10239 Sum of all elements:10239 PHPsum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21032 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21033 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21034 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21035
sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21036 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21037 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21038 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 16 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21040 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21041 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 19
sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2101 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21046 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21047
sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21049 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21051 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Sum of all elements:10232 Sum of all elements:10233_______0_______55 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21047 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21055 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21058 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21040 using 3sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21055 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21062 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 19 Sum of all elements:10236_______0_______46 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 139_______0_______46 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21069 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21055 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21071 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Sum of all elements:10239
sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Sum of all elements:10231 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21046 using 3Sum of all elements:10239
sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21079 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21040 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21081 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21082 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21083 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21084 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21085 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 16 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21040 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21071
sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21089 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21090 Javascriptsum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21091 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21092 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21034 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21035
sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21036 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21037 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21038 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21098 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 19
sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2101 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Sum of all elements:102303
sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21049 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21051 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Sum of all elements:10232 Sum of all elements:102310 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 19 Sum of all elements:10236_______21_______7 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Sum of all elements:10239
sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 2100 Sum of all elements:10231 Sum of all elements:10232 Sum of all elements:10239
sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21079 Sum of all elements:102322 Sum of all elements:102323 sum of elements in ith row 0th row 1 1 -> 20 1st row 1 1 2 -> 21 2nd row 1 2 1 4 -> 22 3rd row 1 3 3 1 8 -> 23 4th row 1 4 6 4 1 16 -> 24 5th row 1 5 10 10 5 1 32 -> 25 6th row 1 6 15 20 15 6 1 64 -> 26 7th row 1 7 21 35 35 21 7 1 128 -> 27 8th row 1 8 28 56 70 56 28 8 1 256 -> 28 9th row 1 9 36 84 126 126 84 36 9 1 512 -> 29 10th row 1 10 45 120 210 256 210 120 45 10 1 1024 -> 21083 Pascal's triangle 0th row 1 1st row 1 1 2nd row 1 2 1 3rd row 1 3 3 1 4th row 1 4 6 4 1 5th row 1 5 10 10 5 1 6th row 1 6 15 20 15 6 1 7th row 1 7 21 35 35 21 7 1 8th row 1 8 28 56 70 56 28 8 1 9th row 1 9 36 84 126 126 84 36 9 1 10th row 1 10 45 120 210 256 210 120 45 10 124
Sum of all elements:102326 Sum of all elements:102327 đầu ra. Sum of all elements:1023
Thời gian phức tạp. TRÊN) giải pháp hiệu quả.
Vì vậy, hãy tính 2n thay vì tính mọi lũy thừa của 2 cho đến (n – 1) và từ ví dụ trên, tổng lũy thừa của 2 cho đến (n – 1) sẽ là (2n – 1) Tổng các hàng trong tam giác Pascal là bao nhiêu?Tổng mỗi hàng của tam giác Pascal là lũy thừa 2 . Trên thực tế, tổng các mục ở hàng thứ n là 2n.
Tổng của tam giác Pascal là gì?Tổng các số trên một đường chéo của tam giác Pascal bằng số bên dưới tổng cuối cùng . Ví dụ: 1 + 2 = 3, 1 + 2 + 3 = 6, 1 + 3 = 4, 1 + 3 + 6 = 10, v.v.
Tổng của hàng thứ 5 trong Tam giác Pascal là bao nhiêu?Tổng = 1+4+6+4+1 = 16 . |