设A=1/2+3/2^2+5/2^3+...+(2n-1)/2^n则2A=1+3/2+5/2^2+7/2^3+…+(2n-1)/2^(n-1)两式相减,得A=1+2/2+2/2^2+2/2^3+…+2/2^(n-1)-(2n-1)/2^n=1+1[1-(1/2)^n-1]/(1-1/2)-(2n-1)/2^n=1+2-1/2^(n-2)-(2n-1)/2^n=3-(2n+3)/2...