Question

Exercitiul 2 , multumesc mult :* :*

Answer 1

$= \frac{\sqrt{3}}{\sqrt{1} \cdot \sqrt{3}}- \frac{\sqrt{1}}{\sqrt{1} \cdot\sqrt{3}} + \frac{\sqrt{5}}{\sqrt{3} \cdot \sqrt{5}} - \frac{\sqrt{3}}{\sqrt{3} \cdot \sqrt{5}} + \frac{\sqrt{7}}{\sqrt{5} \cdot \sqrt{7}}- \frac{\sqrt{5}}{\sqrt{5} \cdot \sqrt{7} } + \frac{ \sqrt{9}}{\sqrt{7} \cdot \sqrt{9}}- \frac{\sqrt{7}}{\sqrt{7} \cdot \sqrt{9}}=$

$= \frac{1}{\sqrt{1}}- \frac{1}{\sqrt{3}}+ \frac{1}{\sqrt{3}}- \frac{1}{\sqrt{5}}+ \frac{1}{\sqrt{5}}- \frac{1}{\sqrt{7}}+ \frac{1}{\sqrt{7}}- \frac{1}{\sqrt{9}}= \\ \\ =1- \frac{1}{\sqrt{9}}= \\ \\ =1- \frac{1}{3} = \\ \\ = \frac{2}{3}.$