Question

arătați ca nr. 2015+2×(1+2+3+.....+2014este pătrat perfect

Answer 1

$Aplicam~ suma~ lui~ Gauss:\\2015+2\cdot (1+2+3+\ldots+2014)=2015+2\cdot \dfrac{2014\cdot 2015}{2}=\\2015+2014\cdot 2015=2015(2014+1)=2015^2,\text{patrat perfect.}$