Question

1-2+2^2-2^3+2^4-2^5+.+2^998-2^999+2^1000

Answer 1

A=1-2+2^2-2^3+....-2^999+2^1000

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

=>3A=2^1001+1

=>A=(2^1001+1)/3