JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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The sum of infinite terms of the series

\frac{1}{{\left( {1 + a} \right)\left( {2 + a} \right)}} + \frac{1}{{\left( {2 + a} \right)\left( {3 + a} \right)}} + \frac{1}{{\left( {3 + a} \right)\left( {4 + a} \right)}} + ... + \mathrm{to}\;\infty

, where

a

is a constant, is

View answer and explanation

Correct option: A

\frac{1}{{1 + a}}

Option A (

\frac{1}{{1 + a}}

) is correct because the series telescopes, and the limit of the partial sum as n approaches infinity is

\frac{1}{{1 + a}}

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