Question

Aratati ca 2+4+6+...+100 nu este patrat perfect.

Answer 1

$\displaystyle 2+4+6+...+100 \\ \text{factor comun pe 2} \\ \\ 2(1+2+3+...+50)= \\ \\ \text{in paranteza aplic gaus} \\ \\ \frac{n(n+1)}{2} = \frac{50\cdot 51}{2}=25 \cdot 51 \\ \\ 2 \cdot 51 \cdot 51 = \\ \\ 50 \cdot 51= \\ \text{Nu este patrat perfect.}$