Question

aratati ca nr. 2005+2×(1+2+3+......+2004)este patrat perfect

Answer 1

[tex]2005+2*(1+2+3+4+...+2004)=\\ 2005+\not2*\frac{2004*2005}{\not2}=\\ 2005+2004*2005=\\ 2005(1+2004)=2005^2[/tex]

Answer 2

$\displaystyle 2005+2 \cdot (1+2+3+...+2004)=2005+2 \cdot \frac{2004(2004+1)}{2} = \\ \\ =2005 +2 \cdot \frac{2004 \cdot 2005}{2} =2005+\not 2 \cdot \frac{4018020}{\not 2} =2005+4018020= \\ \\ =2005(1+2004)=2005 \cdot 2005=2005^2-p.p$