Question

aratati ca nr 2005+2x(1+2+3+.........+2004) e patrat perfect

Answer 1

2005+2•(1+2+3+......+2004)=2005+2•2005•2004:2=2005+2005•2004= 2005•(1+2004)=2005•2005=2005 la puterea 2 este patrat perfect

Answer 2

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