Question

Va rog frumos am nevoie de ajutor!!!!!!
Aratati ca n=2+4+6+....+512-16² este patrat perfect

Answer 1

$N=2+4+6+...+512-16^2= \\ \\ ~~~~=2(1+2+3+...+256)-256= \\ \\ ~~~~=2 \cdot \frac{256 \cdot 257}{2}-256= \\ \\ ~~~~=256 \cdot 257 -256= \\ \\ ~~~~ = 256(257-1)= \\ \\ ~~~~=256 \cdot 256= \\ \\ ~~~~=256^2~-patrat~perfect.$