Question

已知数列{an}的前n项和为Sn且an=n乘以2的n次方，则Sn=?

Answer 1

2+(n-1)×2的n+1次方

Answer 2

Sn=1·2^1+2·2^2+3·2^3+……+n·2^n
2Sn=1·2^2+2·2^3+……+(n-1)·2^n+n·2^(n+1)
∴Sn=2Sn-Sn=-2^1-2^2-2^3-……-2^n+n·2^(n+1)

=-(2^(n+1)-2)+n·2^(n+1)

=(n-1)·2^(n+1)+2