A=2^2+2^3+2^4+........................+2^1000
=> 2A=2^3+2^4+........................+2^1001
=> 2A-A=A=(2^3+2^4+........................+2^1001)-(2^2+2^3+2^4+........................+2^1000)
=> A=2^1001-2^2
A=2^2+2^3+2^4+........................+2^1000
=> 2A=2^3+2^4+........................+2^1001
=> 2A-A=A=(2^3+2^4+........................+2^1001)-(2^2+2^3+2^4+........................+2^1000)
=> A=2^1001-2^2