Question

Arătaţi că numărul b=1+3+5+...+2011 e pătrat perfect.

Answer 1

[tex]b=1+3+5+...+2011\\ b=1+2+3+...+2011-2-4-6-...-2010\\ b=\frac{2011*2012}{2}-2(1+2+3+...+1005)\\ b=2011*1006-\not2*\frac{1005*1006}{\not2}\\ b=2011*1006-1005*1006\\ b=1006(2011-1005)=\ \textgreater \ b=1006^2[/tex]

Answer 2

1+2+3+...+2011-(2+4+6+...+1005)=2011 x 2012 - 2 x (1+2+3+...+1005) cred.