JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Easy

1 of 1

Analyzing +4 | -1

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

are in arithmetic progression, where

{a_1} > 0

for all

i

.

Then,

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

is equal to

View answer and explanation

Correct option: B

\frac{{n - 1}}{{\sqrt {{a_1}} + \sqrt {{a_n}} }}

Option B (

\frac{{n - 1}}{{\sqrt {{{{a_1}}}} + \sqrt {{{{a_n}}}} }}

) is the correct answer. The sum telescopes after rationalizing each term, and the common difference allows simplification to the final expression.

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