If ${S_n} = \frac{1}{{6.11}} + \frac{1}{{11.16}} + \frac{1}{{16.21}} + ...{\rm{to}}\;n$ terms, then $6{S_n}$ equals

$\frac{1}{{\left( {5n + 6} \right)}}$

JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Application +4 | -1

{S_n} = \frac{1}{{6.11}} + \frac{1}{{11.16}} + \frac{1}{{16.21}} + ...\mathrm{to}\;n

terms, then

6{S_n}

equals

View answer and explanation

Correct option: B

\frac{n}{{\left( {5n + 6} \right)}}

Option B is correct because the series can be expressed as a telescoping series, allowing for simplification and direct calculation of the sum.

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