1/2+1/2+3/8+...+n/2n次方=

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1/2+1/2+3/8+...+n/2n次方=
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1/2+1/2+3/8+...+n/2n次方=
1/2+1/2+3/8+...+n/2n次方=

1/2+1/2+3/8+...+n/2n次方=
设 S=1/2+2/4+3/8+……+n/2^n
1/2*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
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