If ${S_n} = \mathop \sum \limits_{k = 1}^n \,\,{a_k}$ and $\mathop {\lim }\limits_{n \to \infty } {a_n} = a$, then $\mathop {\lim }\limits_{n \to \infty } \frac{{{S_{n + 1}} - {S_n}}}{{\sqrt {\mathop \sum \nolimits_{k = 1}^n \,k} }}$ is equal to

JEE MATHEMATICS MCQ: LIMITS

1 Easy

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Analyzing +4 | -1

{S_n} = \sum \limits_{k = 1}^n \,\,{a_k}

and

\lim\limits_{n \to \infty } {a_n} = a

, then

\lim\limits_{n \to \infty } \frac{{{S_{n + 1}} - {S_n}}}{{\sqrt {\sum \nolimits_{k = 1}^n \,k} }}

is equal to

View answer and explanation

Correct option: A

Option A (0) is correct because the limit of the given expression as n approaches infinity is 0.

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