The value of $\mathop {\lim }\limits_{n \to \infty } \frac{1}{n}\sum\limits_{r = 0}^{2n - 1} {\frac{{{n^2}}}{{{n^2} + 4{r^2}}}} $ is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

The value of

\lim\limits_{n \to \infty } \frac{1}{n}\sum\limits_{r = 0}^{2n - 1} {\frac{{{n^2}}}{{{n^2} + 4{r^2}}}}

View answer and explanation

Correct option: B

\frac{1}{2}{\tan ^{ - 1}}(4)

Option B is correct because the limit of the Riemann sum can be expressed as a definite integral, which evaluates to

\frac{1}{2}{\tan ^{ - 1}}(4)

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