A= 1+2^2+2^3+2^4+2^5+...+2^100+2
2A = 2 + 2^3 + 2^4 + 2^5 + 2^6 +.....+ 2^101 + 2^1
2A - A = ( 2 + 2^3 + 2^4 + 2^5 + 2^6 +.....+ 2^101 + 2^1) - ( 1 + 2^2 + 2^3 + 2^4 + 2^5 +...+ 2^100 + 2 )
A = 2^101 + 2^1 - 1 + 2^2
A = 2^102 - 1 + 2^2
A = 2^102 + 2^2 -1
A= 2^104 - 1
B= 3 + 3^2 + 3^3 +...+ 3^100
3B = 3^2 + 3^3 + 3^4 +....+ 3^101
3B - B = ( 3^2 + 3^3 + 3^4 +....+ 3^101 ) - ( 3 + 3^2 + 3^3 +...+ 3^100 )
2B = 3^101 - 3
B = 3^101 -3
2
