The $\lim _\limits {n \rightarrow \infty} S_n$ if $ S_n=\frac{1}{2 n}+\frac{1}{\sqrt{4 n^2-1}}+\frac{1}{\sqrt{4 n^2-4}}+\ldots+\frac{1}{\sqrt{3 n^2+2 n-1}} $ is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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The

\lim \limits_{{n \rightarrow \infty}} S_n

S_n=\frac{1}{2 n}+\frac{1}{\sqrt{4 n^2-1}}+\frac{1}{\sqrt{4 n^2-4}}+\ldots+\frac{1}{\sqrt{3 n^2+2 n-1}}

View answer and explanation

Correct option: D

\pi / 6

Option D (

\pi / 6

) is correct because the limit of the given sum can be expressed as a definite integral, which evaluates to

\pi/6

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