Question

2 la puterea 1 + 2² +2³ +..+2 la puterea 2014

Answer 1

[tex]S=2^1+2^2+2^3+...+2^{2013}+2^{2014}\ \ \ \text{inmultim cu 2 in ambii membri}\\ 2S = \underbrace{2^2+2^3+2^4+...+2^{2014}}_{S-2^1}+2^{2015}\\\\ 2S=S-2^1+2^{2015}\\ S=2^{2015}-2=\boxed{2(2^{2014}-1)}[/tex]