JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Easy

1 of 1

Application +4 | -1

The sum to

n

terms of the series

\frac{1}{\sqrt{7}+\sqrt{10}}+\frac{1}{\sqrt{10}+\sqrt{13}}+\frac{1}{\sqrt{13}+\sqrt{16}}+\cdots

View answer and explanation

Correct option: A

\frac{1}{3}(\sqrt{7+3 n}-\sqrt{7})

Option A (

\frac{{1}}{{3}}(\sqrt{{7+3n}}-\sqrt{{7}})

) is correct because rationalizing the denominator of each term and summing the telescoping series leads to this result.

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