设 S=1/2+2/4+3/8+……+n/2^n1/2*S=1/4+2/8+……+(n-1)/2^n+n/2^(n+1)两式想减得：1/2*S=1/2+1/4+1/8+……+1/2^n-n/2^(n+1)=1/2*(1-(1/2)^n)÷ (1-1/2)-n/2^(n+1)=1-1/2^n-n/2^(n+1)∴ S=2-1/2^(n-1)-n/2^n手机提问...