- A=1+3/2^3+4/2^4+5/2^5+...100/2^100 1/2*A = 1/2 + 3/2^4 + 4/2^5 +....+ 99/2^100 +100/2^101. A- A/2 = 1/2A =1/2 + 3/2^3 + 1/2^4 +...+1/2^100 - 100/2^101= = [1/2+1/2^2 +1/2^3+...+1/2^100] -100/2^101 (Do 3/2^3 = 1/2^2 +1/2^3) =[1-(1/2)^101]/(1-1/2) -100/2^101 = =(2^101 -1)/2^100 - 100/2^101