Question:medium

The value of $ \sum_{k=1}^{n} \frac{1}{\sqrt{a_{k}} + \sqrt{a_{k+1}}} $, where $ a_{1}, a_{2}, \dots, a_{n} $ are in A.P. with common difference $ d $, is:

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Rationalization often turns a complex sum into a simple telescoping series.

Updated On: Apr 8, 2026

$\frac{n}{\sqrt{a_{1}} + \sqrt{a_{n+1}}}$
$\frac{n-1}{\sqrt{a_{1}} + \sqrt{a_{n}}}$
$\frac{n}{\sqrt{a_{1}} - \sqrt{a_{n+1}}}$
$\frac{n+1}{\sqrt{a_{1}} + \sqrt{a_{n+1}}}$

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The Correct Option is A

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The value of \( \sum_{k=1}^{n} \frac{1}{\sqrt{a_{k}} + \sqrt{a_{k+1}}} \), where \( a_{1}, a_{2}, \dots, a_{n} \) are in A.P. with common difference \( d \), is:

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The Correct Option is A

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