Question

Care este rezultatul ?

Answer 1

2015+2x(1+2+...+2014)=2015+2x(2014x2015)/2=2015+2014x2015=
=2015(1+2014)=2015x2015=patrat perfect
.
S-a folosit: 1+2+...+n=n(n+1)/2 si apoi s-a dat factor comun.

Answer 2

$\displaystyle 2015+2 \cdot (1+2+3+...+2014)=2015+\not 2 \cdot \frac{2014(2014+1)}{\not2} = \\ \\ =2015+ 2014 \cdot 2015=2015(1+2014)=2015 \cdot 2015=2015^2=p.p.$