已知an=n/3n,则数列｛an｝的前n项和Sn等于多少?

Sn=1/3+2/(3^2)+3/(3^3)+.+n/(3^n)
(1/3)Sn=1/(3^2)+2/(3^3)+.+(n-1)/(3^n)+n/[3^(n+1)]
两式相减得(2/3)Sn=1/3+1/(3^2)+.+1/(3^n)-n/[3^(n+1)]
=(1/3)[1-(1/3)^n]/[1-(1/3)]-n/[3^(n+1)]
= 1/2-1/2*[(1/3)^n]-n/[3^(n+1)]
Sn=3/4-3/4*[(1/3)^n]-3/2*n/[3^(n+1)]