Question

Aratati ca numarul 2005+2 x(1+2+3+....+2004) este patrat perf

Answer 1

2005+2[1002·2005]
2005+2004·2005
⇒2005[1+2004]
⇒2005·2005=2005²⇒patrat perfect;

Answer 2

2005+2(1+2+3+...+2004)=2005+2*(2004*2005)/2=2005+2004*2005=2005(1+2004)=2005*2005=$2005^{2}$- pătrat perfect.