Question

已知数列an=n^(an等于n的平方),求数列和Sn=?

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

相加,左边中间正负抵消

(n+1)³+1=3(1²+2²+……+n²)+3(1+2+……+n)+n

1+2+……+n=n(n+1)/2

代入整理得

1²+2²+……+n²=n(n+1)(2n+1)/6