Question

Aratati ca √1+3+5+...+2013 apartine Q

Answer 1

$\sqrt{1 + 3 + 5 + ... + 2013} =$

1+3+5+...+2013=

= 1+2+3+...+2013- (2+4+...+2012)=

= 1+2+3+...+2013- 2(1+2+...+1006)=

$= \frac{2013 \times 2014}{2} - 2 \times \frac{1006 \times 1007}{2} =$

$= 2013 \times 1007 - 1006 \times 1007 =$

$= 1007(2013 - 1006) =$

$= 1007 \times 1007 = {1007}^{2}$

$\sqrt{ {1007}^{2} } = 1007$

=>1007€Q

Answer 2

Explicație pas cu pas:

Prima parte de jos si a doua de sus.