[tex] \sqrt{1 + 3 + 5 + ... + 2013} =[/tex]
1+3+5+...+2013=
= 1+2+3+...+2013- (2+4+...+2012)=
= 1+2+3+...+2013- 2(1+2+...+1006)=
[tex] = \frac{2013 \times 2014}{2} - 2 \times \frac{1006 \times 1007}{2} = [/tex]
[tex] = 2013 \times 1007 - 1006 \times 1007 =[/tex]
[tex] = 1007(2013 - 1006) = [/tex]
[tex] = 1007 \times 1007 = {1007}^{2} [/tex]
[tex] \sqrt{ {1007}^{2} } = 1007[/tex]
=>1007€Q
