Question

Arătați ca 201+2×(1+2+3+4+.........+200) este patrat perfect

Answer 1

$201+2(1+2+3+...+200)=201+\frac{2*200*201}{2}=201+200*201=201*201=201^2 -este \ p.p$

Answer 2

[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]