1到n平方和

Question

1到n的平方和

Answer 1

1到n的平方和为 n(n+1)(2n+1)/6

Answer 2

解 1+2^2+...+n^2=n(n+1)(2n+1)/6 证明：当n=1的时候 左边=1^2=1 右边=1(1+1)(2+1)/6=1 成立设当n的时候成立 则1+2^2+...n^2=n(n+1)(2n+1)/6 则n+1的时候左边=1+2^2+...+n^2+(n+1)^2 =n(n+1)(2n+1)/6 +(n+1)^2 =(n+1)/6 * (2n^2+n+6(n+1)) =(n+1)(2n^2+7n+6)/6 =1/6*(n+1)(n+2)(2n+3) =1/6*(n+1)(n+1+1)(2(n+1)+1) 成立