Question

Aratati ca numarul 2012+2×(1+2+3+4+...+2011) este patrat perfect

Answer 1

2012+2012*2011=2012(1+2011)=2012*2012---patrat perfect

Answer 2

$2012+2*(1+2+3+4+...+2011)=\ \textgreater \ patrat~perfect$
[tex]=2012+2 * \frac{2011*(2011+1)}{2} [/tex]
[tex]=2012+2012*2011 [/tex]
$=2012*(1+2011)$
$=2012*2012$
$=2012^2=\ \textgreater \ patrat~perfect$