Question

1²+2²+3²+……+n²的n项求和

1²+2²+3²+……+n²的n项求和求详细步骤

Answer 1

1²+2²+3²+……+n²的n项求和的详细步骤如下：

答由(n+1)^3=n^3+3n^2+3n+1
可将n=1,2,3....n代入得n个等式

2^3=1^3+3x1^2+3x1+1
3^3=2^3+3x2^2+3x2+1
4^3=3^3+3x3^2+3x3+1
……
(n+1)^3=n^3+3xn^2+3xn+1

两边相加可得:1^2+2^2+……+n^2=n(n+1)(2n+1)/6

Answer 2

收

Answer 3

1²+2²+3²+……+n²的n项求和
1²+2²+3²+……+n²
=(1/6)n(n+1)(2n+1).

Answer 4

由(n+1)^3=n^3+3n^2+3n+1
将n=1,2,3....n代入得n个等式

2^3=1^3+3x1^2+3x1+1
3^3=2^3+3x2^2+3x2+1
4^3=3^3+3x3^2+3x3+1
……
(n+1)^3=n^3+3xn^2+3xn+1
两边相加可得:1^2+2^2+……+n^2=n(n+1)(2n+1)/6

Answer 5

n^2=(n+1)*n-n
=2*Sigma C(n+1,2) - 2*Sigma n