CAT 2019 Quant Question with Solution 9

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

  1. $\frac{n-1}{\sqrt{a_{1}}+\sqrt{a_{n-1}}}$
  2. $\frac{n}{\sqrt{a_{1}}+\sqrt{a_{n+1}}}$
  3. $\frac{n-1}{\sqrt{a_{1}}+\sqrt{a_{n}}}$
  4. $\frac{n}{\sqrt{a_{1}}-\sqrt{a_{n+1}}}$
Show Answer

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.


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