JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Easy

1 of 1

Application +4 | -1

a_{1}, a_{2}, a_{3}, \ldots, a_{n}

are in AP, where

a_{i} > 0

for all

i

, then the value of

\frac{1}{\sqrt{a_{1}}+\sqrt{a_{2}}}+\frac{1}{\sqrt{a_{2}}+\sqrt{a_{3}}}+\cdots+\frac{1}{\sqrt{a_{n-1}}+\sqrt{a_{n}}}=

View answer and explanation

Correct option: A

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

Option A (

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

) is correct because rationalizing the terms and using the properties of AP simplifies the expression to

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

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