Question

1+2+4+8+........+2^2015 = ?

Answer 1

$S=2^{0}+2^{1}+2^{2}+2^{3}+...+2^{2015}$

Inmultim relatia cu 2:

$2S=2^{1}+2^{2}+2^{3}+...2^{2015}+2^{2016}$

Dar prima parte din suma face parte din S:

$2S = S - 1 + 2^{2016} ==\ \textgreater \ S = 2^{2016} - 1$