JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Application +4 | -1

{a_1},{a_2},{a_3}, \ldots ,\;{a_n}

are in AP, where

{a_i} > 0

for all i, then value of

\frac{1}{{\sqrt {{a_1}} + \sqrt {{a_2}} }} + \frac{1}{{\sqrt {{a_2}} + \sqrt {{a_3}} }} + ... + \frac{1}{{{a_{n - 1}} + \sqrt {{a_n}} }}

is equal to

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 it is the simplified form of the given series after rationalization and telescoping.

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