sn=n*(n+1)/2 +2*2+3*2^2+……+(n+1)*2^n 用错位相减法的过程

问题描述:

sn=n*(n+1)/2 +2*2+3*2^2+……+(n+1)*2^n 用错位相减法的过程

sn=n*(n+1)/2 +2*2+3*2^2+……+(n+1)*2^n
Sn-1=n(n-1)/2+2*2+3*2^2+……+n*2^(n-1)
an=Sn-Sn-1
= n(n+1)/2 -n(n-1)/2+(n+1)*2^n
=n+(n+1)*2^n