Răspuns :
[tex]201+2(1+2+3+...+200)=201+\frac{2*200*201}{2}=201+200*201=201*201=201^2 -este \ p.p[/tex]
[tex]201+2(1+2+3+4+...+200)=\\
Luam~suma~1+2+3+4+...+200~separat~si~aplicam\\
formula~Suma~Gauss:\\
1+2+3+4+....+200= \frac{200[200+1]}{2}=\ \textgreater \ 100*201=20100\\
Revenim~la~exercitiul~nostru~si~avem:\\
201+2*20100=\ \textgreater \ 201+40200=40401\\
Acum~vedem~daca~acest~numar~este~sau~nu~patrat~perfect:\\
\sqrt{40401} =201=\ \textgreater \ 40401=patrat~perfect.[/tex]
