Question

Aratati ca nr. A=2003+2×(1+2+...........+2002)este patrat perfect

Answer 1

1+2+3+...+2002 = 2002x2003:2             si acum inlocuim acolo sus

A=2003+2x2002x2003:2
A=2003+2002x2003
A=2003x(2002+1)
A=2003x2003  ==> A este patrat perfect

Answer 2

$\displaystyle 2003+2 \times (1+2+...+2002)=2003+2 \times \frac{2002(2002+1)}{2} = \\ \\ =2003+2 \times \frac{2002 \times 2003}{2} =2003+\not2 \times \frac{4010006}{\not2} = \\ \\ =2003+4010006=2003(1+2002)=2003 \times 2003=2003^2-p.p$