Question

If $a_{1}, a_{2}, a_{3}, \ldots, a_{n}$ are in A.P. where $a_{i}>0$ for all $i$, then $\frac{1}{\sqrt{a_{1}}+\sqrt{a_{2}}}+\frac{1}{\sqrt{a_{2}}+\sqrt{a_{3}}}+\ldots .+$ $\frac{1}{\sqrt{a_{n-1}}+\sqrt{a_{n}}}$ is?

• A. $\frac{1}{\sqrt{a_{n}}+\sqrt{a_{1}}}$
• B. $\frac{n}{\sqrt{a_{n}}+\sqrt{a_{1}}}$
• C. $\frac{1- n }{\sqrt{ a _{ n }}+\sqrt{ a _{1}}}$
• D. $\frac{11-1}{\sqrt{a_{1}}+\sqrt{a_{n}}}$

Answer 1

The Correct Option is C

Answer (c) $\frac{1- n }{\sqrt{ a _{ n }}+\sqrt{ a _{1}}}$