Question:
If $a_{1}, a_{2}, \ldots$ are in A.P., then, $\frac{1}{\sqrt{a_{1}}+\sqrt{a_{2}}}+\frac{1}{\sqrt{a_{2}}+\sqrt{a_{3}}}+\cdots+\frac{1}{\sqrt{a_{n}}+\sqrt{a_{n+1}}}$ is equal to
- $\frac{n-1}{\sqrt{a_{1}}+\sqrt{a_{n-1}}}$
- $\frac{n}{\sqrt{a_{1}}+\sqrt{a_{n+1}}}$
- $\frac{n-1}{\sqrt{a_{1}}+\sqrt{a_{n}}}$
- $\frac{n}{\sqrt{a_{1}}-\sqrt{a_{n+1}}}$
Correct Answer: Option: 2
Shortcut:
For such questions, we can take value of n =1. The right option must give the first term i.e. $\frac{1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{2}}}}$
Only option (2) satisfies.
CAT Online Course
Also Check: 841+ CAT Quant Questions with Solutions
