Question

5 puncte
Cum se calculeaza 2+4+6+.......+n

Answer 1

2+4+6+....+n = 2(1+2+3+....n/2) = 2( 1+n/2) (n/2)/2 = n(n+2)/4 ; unde n numar par.

Answer 2

$\text{Primul pas} \to \boxed{\text {1.Il dai pe 2 factor comun.}} \\ ~~~~~~~~~~~~~~~\to \boxed{2.\text{Aplici formula lui Gauss.}} \\ \\ \\ 2+4+6...+n = 2(1+2+3+...+ \dfrac{n}{2}}) \\ \\ Calculezi~separat~1+2+3+....+x = \dfrac{x(x+1)}{2}~si~dupa~inmultesti~rezultatul~cu~2.$