1/2+3/2^2+5/2^3+7/2^4+…+2n-1/2^n

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1/2+3/2^2+5/2^3+7/2^4+…+2n-1/2^n1/2+3/2^2+5/2^3+7/2^4+…+2n-1/2^n1/2+3/2^2+5/2^3+7/2^4+…+2n-1/2^n设s=1

1/2+3/2^2+5/2^3+7/2^4+…+2n-1/2^n
1/2+3/2^2+5/2^3+7/2^4+…+2n-1/2^n

1/2+3/2^2+5/2^3+7/2^4+…+2n-1/2^n
设s=1/2+3/2^2+5/2^3+7/2^4+…+2n-1/2^n
1/2s= 1/2^2+3/2^3+5/2^4+…+2n-3/2^n+2n-1/2^(n+1)
s-1/2s=1/2+2/2^2+2/2^3+2/2^4+…+2/2^n—2n-1/2^(n+1)
1/2s= 1/2+(1/2+1/2^2+1/2^3+…+1/2^n-1)—2n-1/2^(n+1)
=1/2+(1-1/2^n-1)—2n-1/2^(n+1)
s=2(1/2s)=3+7-2n/2^n