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Aratati ca numarul 2005+2.(1+2+3+...+2014) este patrat perfect

Răspuns :

[tex]2005+2*(1+2+3+...+2014)= \\ \\ 2005+2* \frac{2004(2004+1)}{2}= \\ \\ 2005+2004*2005= \\ \\ 2005(1+2004)= \\ \\ 2005*2005= \\ \\ 2005^2=p.p[/tex]