Question

Aratati ca urmatorul nr este patrat perfect:
x=1004+2+4+6+...+2006

Answer 1

x= 1004+2(1+2+3+....+1003) ⇔ $x=1004+2 \frac{1003.1004}{2}$⇔ x= 1004+1003·1004⇔ x= 1004(1+1003)⇔ x=1004·1004⇔ x=$1004^{2}$⇒ x= patrat perfect