Question

a)n=2015+2ori(1+2+3+..+2014)

b)aratati ca n e patrat perfect

Answer 1

În paranteză ai suma lui Gauss
$\frac{2014(2014+1)}{2}$
$2015+2* \frac{2014*2015}{2} = \\ 2015+2014*2015= \\ 2015(1+2014)= \\ 2015^2$
=>n=pătrat perfect

Answer 2

$n=2015+2*(1+2+3+...+2014) \\\\ n=2015+2 *\frac{(1+2014)*2014}{2} \\\\ n=2015+(1+2014)*2014 \\\\ n= 2015+2015*2014 \\\\ n=2015(1+2014) \\\\ n=2015*2015 \\\\ \boxed{n=2015^2\to este \ p.p}$