Sum 1 / 2 + 3 / 4 + 5 / 8 +. + (2n-1 / 2)

Sum 1 / 2 + 3 / 4 + 5 / 8 +. + (2n-1 / 2)

--------------------------------------------------------------=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^n