JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Application +4 | -1

S_k=\lim \limits_{{n \rightarrow \infty}} \sum\limits_{{i=0}}^n \frac{1}{(k+1)^i}

, then

\sum\limits_{{k=1}}^n k S_k

is equal to

View answer and explanation

Correct option: D

\frac{n(n+3)}{2}

Option D (n(n+3)/2) is correct because it is the result of simplifying the summation after finding that S_k = (k+1)/k.

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