求和Sn=1/2+2/4+3/8+…+n/2^n,不明白Sn-1/2Sn是怎样减得

问题描述:

求和Sn=1/2+2/4+3/8+…+n/2^n,不明白Sn-1/2Sn是怎样减得
不明白Sn-1/2Sn是怎样减得,
Sn-1/2Sn=1/2+1/4+1/8+....+1/2^n- n/2^(n+1) 怎么来的?

Sn=1/2+2/4+3/8+…+n/2^n1/2Sn= 1/4+2/8+…+(n-1)/2^n+n/2^(n+1)Sn-1/2Sn=1/2+1/4+1/8+.+1/2^n- n/2^(n+1)1/2Sn=1-1/2^n-n/2^(n+1)=[2^(n+1)-n-2]/2^(n+1)Sn=[2^(n+1)-n-2]/2^n=2-(n+2)/2^n