数列 1+(1+1/2)+(1+1/2+1/4)+..............=?

1+1/2+1/4+.............=2*[1-(1/2)^n] 等比数列
所以1+(1+1/2)+(1+1/2+1/4)+..............=2*[(1-1/2)+(1-1/4)+……〕=2*[n-(1/2+1/4+……)]=2n-1+(1/2)^n

通象公式An=[2(2)(n-1)-1]/(2)(n-1)=(2)n-1/(2)(n-1)=2-1/(2)(n-1)
<(2)(n-1)是2的n-1次方>
1+(1+1/2)+(1+1/2+1/4)+..............=2n-[1+1/2+1/4+1/8+..1/(2)(n-1)]=2n-(等比数列求和,公式我忘了.)