- 一道数列求和问题1/2+2/4+3/8+……+n/(2^n)
- 1/2+2/4+3/8+……+n/(2^n)
- Sn=1/2+2/4+3/8+...+n/2^n....<1>
Sn/2=1/4+2/8+3/16+.....+n/2^(n+1)....<2>
<1>-<2>得:Sn/2=1/2+1/4+1/8+1/16+.....+1/2^n-n/2^(n+1)
所以Sn=1+1/2+1/4+1/8+....+1/2^(n-1)-n/2^n
而1+1/2+1/4+1/8+。。。。+1/2^(n-1)是等比数列,所以
Sn=2-2(1/2)^n-n/2^n=2-(n+2)/2^n