JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Application +4 | -1

\sum \limits_{n = 1}^\infty \frac{1}{{\left( {n + 1} \right)\left( {n + 2} \right) \ldots \left( {n + k} \right)}}

is equal to

View answer and explanation

Correct option: C

\frac{1}{{\left( {k - 1} \right)k!}}

Option A (

\frac{1}{{\left( {k - 1} \right)\left( k! \right)}}

) is correct because it is the result of the infinite summation of the given series using partial fraction decomposition.

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