Question

What is the value of
$\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+.......+\frac{1}{\sqrt{15}+\sqrt{2}}$?

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is D $3$

$\frac{1}{\sqrt{2}+1}+\frac{1}{\sqrt{3}+\sqrt{2}}+...+\frac{1}{\sqrt{16}+\sqrt{15}}$

Rationalisation

$\Rightarrow \frac{\sqrt{2}-1}{1}+\frac{\sqrt{3}-\sqrt{2}}{1}+\frac{\sqrt{4}-\sqrt{3}}{1}+...+\frac{\sqrt{16}-\sqrt{15}}{1}$

$\Rightarrow \sqrt{16}-1\Rightarrow 3$