Question

Demonstrati ca numarul n = 2007 + 2 . ( 1 + 2 + 3 + ... + 2006) este patrat perfect

Answer 1

n=2007 + 2*(1+2006)*2006/2

n=2007 + 2007 *2006

n=2007(1+2006)

n=2007*2007

n=2007²  -este pp

Answer 2

1+2+3+....+n=n(n+1):2 ⇒ 1+2+3+...+2006=2006*2007:2=1003*2007
n=2007+2*1003*2007=2007(1+2006)=2007^2
Daca n=x^2= 2007^2 rezulta ca n este patrat perfect