Question

Cum rezolv 1+2+4+.....+2la puterea 40??
Am nevoie rapid!

Answer 1

$S=2^0+2^1+2^2+...+2^{40}$

Inmultim relatia cu 2:

$2S=2^1+2^2+2^3+...+2^{40}+2^{41}$

Dar primele elemente mai putin ultimul, reprezinta S - 1

[tex]2S = (S-1)+2^{41}\\ S=2^{41}-1[/tex]