Sn=1/2+2/2^2+3/2^3+4/2^4……+n/2^n
(1/2)*Sn= 1/2^2+2/2^3+3/2^4……+(n-1)/2^n+n/2^(n+1)
联立二式,得(1/2)*Sn=1/2+1/2^2+1/2^3+……+1/2^n-n/2^(n+1)=1-1/2^n-n/2^(n+1)
Sn=2-1/2^(n-1)-n/2^n