Question

1+2+2^2+2^3+.....2^100+2^101.Repedee va rogg

Answer 1

Notam suma cu S.

$S=1+2+2^2+\ldots +2^{101} |\cdot 2\\2S=2+2^2+2^3+\ldots +2^{102}\\----------------------\\2S-S=2^{102}-1 (\text{termenii se reduc})\\\boxed{S=2^{102}-1}$