Question

The sum of n terms of the series, $\frac{1}{\sqrt{1}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{7}}+..........$ is

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

$\frac{1}{\sqrt{1}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{7}}+....+\frac{1}{\sqrt{2n-1}+\sqrt{2n+1}}\Rightarrow \left[\frac{\sqrt{3}-1}{2}\right]+\left[\frac{\sqrt{5}-\sqrt{3}}{2}\right]+\left[\frac{\sqrt{7}-\sqrt{5}}{2}\right]+....+\left[\frac{\sqrt{2n+1}-\sqrt{2n-1}}{2}\right]\Rightarrow \frac{\sqrt{2n+1}-1}{2}$