Question

A=2×(1+2+3.....+2015)+2016 este patrat perfect.
Va rog rapid dau coroana.

Answer 1

   
[tex]\displaystyle\\ A=2\times(1+2+3+\cdots+2015)+2016 =\\\\ =2\times \frac{2015(2015+1)}{2} +2016 =\\\\ =2\times \frac{2\times2015\times 2016)}{2}+2016 =~~~\text{(Simplificam fractia cu 2)}\\\\ =2015\times 2016+2016=~~~\text{(Dam factor comun pe 2016)}=\\\\ = 2016(2015 + 1) = 2016\times 2016 = \boxed{\bf 2016^2 = pp}[/tex]