数列｛n²｝前n项和推导过程

数列｛n²｝前n项和推导过程
数列｛n²｝前n项和推导过程

数列｛n²｝前n项和推导过程
n^2 = n(n+1) -n
= (1/3)[ n(n+1)(n+2)- (n-1)n(n+1) ] - (1/2)[n(n+1) - (n-1)n]
∑(i:1->n) i^2
=∑(i:1->n) {(1/3)[ i(i+1)(i+2)-(i-1)i(i+1) ] - (1/2)[i(i+1) - (i-1)i] }
=(1/3)n(n+1)(n+2) -(1/2)n(n+1)
= (1/6)n(n+1)(2n+1)