Question

1+2^1+2^2+2^3+. +2^100=.

Answer 1

Explicație pas cu pas:

$S = 1 + 2 + 2^{2} + 2^{3} + ... + 2^{100} \ \ \Big| \cdot 2$

$2S = 2 + 2^{2} + 2^{3} + 2^{4} + ... + 2^{100} + 2^{101} \ \ \Big| + 1$

$2S + 1 = \underbrace{1 + 2 + 2^{2} + 2^{3} + 2^{4} + ... + 2^{100}}_{S} + 2^{101}$

$2S + 1 = S + {2}^{101} \implies S = {2}^{101} - 1$