Sn=1/2+2/4+3/8+……+n/2^n
两边同乘2
2Sn=1+2/2+3/4+……+n/2^(n-1)
两式错位相减,即2/2-1/2,3/4-2/4,4/8-3/8……
Sn=1+[1/2+1/4+1/8+……+1/2^(n-1)]-n/2^n
=1+1/2×(1-(1/2)^(n-1))/(1-1/2)-n/2^n
=2-(n+2)/2^n