Question

Aratati ca numarul 2013 +2(1+2+ ......2012) este patrat perfect .
Va rog ! :*

Answer 1

 2013 +2(1+2+ ......2012)=
= 2013 +2*2012(2012+1)/2=
= 2013 +2*1006*2013=
= 2013 +2012*2013=
= 2013(1 +2012)=
=2013*2013=
=2013²

Answer 2

2013 + 2 x ( 1+2+...+ 2012)=
1 + 2+ ... + 2012 = 
=(2012 x 2013) : 2=
=4050156:2=
=2025078

2013+ 2 x 2025078=
= 2013+ 4050156=
= 4052169
$2013^{2}$