Question

如何求通项公式为N方的数列的前n项和.要有详细步骤

Answer 1

(n+1)³-n³=3n²+3n+1

n³-(n-1)³=3(n-1)²+3(n+1)+1

……

2³-1³=3*1²+3*1+1

全都加起来

左边正负抵消

(n+1)³-1³=3*(1²+2²+……+n²)+3*(1+2+……+n)+1*n

1+2+……+n=n(n+1)/2

则(n+1)³-1=3*(1²+2²+……+n²)+3n(n+1)/2+n

整理得1²+2²+……+n²=n(n+1)(2n+1)/6