Question

Calculeaza:
$\sqrt{ \frac{1+3+5+...+2015}{1+3+5+...+2017} }$

Answer 1

[tex]\it 1+3+5+\ ...\ +2015 = \left(\dfrac{2016}{2}\right)^2= 1008^2 \\\;\\ 1+3+5+\ ...\ +2017 = \left(\dfrac{2018}{2}\right)^2= 1009^2[/tex]

Expresia din enunț devine :

$\it \sqrt{\dfrac{1008^2}{1009^2}} =\dfrac{1008}{1009}$