化简算式1/2^2+2/2^3+3/2^4+……+[n-1]/2^n+n/2^[n+1}如何化为1/2+1/2^2+……+1/2^n-n/2^[n+1}

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化简算式1/2^2+2/2^3+3/2^4+……+[n-1]/2^n+n/2^[n+1}如何化为1/2+1/2^2+……+1/2^n-n/2^[n+1}
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化简算式1/2^2+2/2^3+3/2^4+……+[n-1]/2^n+n/2^[n+1}如何化为1/2+1/2^2+……+1/2^n-n/2^[n+1}
化简算式
1/2^2+2/2^3+3/2^4+……+[n-1]/2^n+n/2^[n+1}如何化为1/2+1/2^2+……+1/2^n-n/2^[n+1}

化简算式1/2^2+2/2^3+3/2^4+……+[n-1]/2^n+n/2^[n+1}如何化为1/2+1/2^2+……+1/2^n-n/2^[n+1}
设:
s= 1/2^2+2/2^3+3/2^4+……+[n-1]/2^n+n/2^[n+1]
2s=1/2+2/2^2+3/2^3+…… ……+n/2^n
s=2s-s=1/2+1/2^2+……+1/2^n -n/2^[n+1]
=1-1/2^n -n/2^[n+1]