Question

S=2° +2¹ +2² +2³+...+2⁹⁹.

Answer 1

Explicație pas cu pas:

$S = {2}^{0} + {2}^{1} + 2^{2} + 2^{3} + ... + 2^{99} \ \ \Big| \cdot 2$

$2S = 2 + 2^{2} + 2^{3} + 2^{4} + ... + 2^{99} + 2^{100} \ \ \Big| + 1$

$2S + 1 = \underbrace{1 + 2 + 2^{2} + 2^{3} + 2^{4} + ... + 2^{99}}_{S} + 2^{100}$

$2S + 1 = S + {2}^{100} \implies S = {2}^{100} - 1$