JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Sum to n terms of the series

\frac{1}{{1\;.\;\;2\;.\;\;3\;.\;\;4}} + \frac{1}{{2\;.\;\;3\;.\;\;4\;.\;\;5\;}} + \frac{1}{{3\;.\;\;4\;.\;\;5\;.\;6\;}} + \ldots ,

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Correct option: D

\frac{{{n^3} + 6{n^2} + 11n}}{{18\left( {n + 1} \right)\left( {n + 2} \right)\left( {n + 3} \right)}}

Option D (

\frac{{{n^3} + 6{n^2} + 11n}}{{18\left( {n + 1} \right)\left( {n + 2} \right)\left( {n + 3} \right)}}

) is correct because it represents the sum to n terms of the given series after using partial fractions.

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