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Demonstrati ca numarul : 2006 + 2 (1+2+3+...+2005) este patrat perfect.

Răspuns :

 2006 + 2×(1+2+3+...+2005)=
=2006+2
×2005×2006/2=
=2006+2005×2006=
=2006×(1+2005)=
=2006×2006=
=2006²
=2006+2×2005×2006/2
=2006+2005×2006
=2006(1+2005)
=2006×2006
=2006²