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The value of \(\lim _{n \rightarrow \infty} \frac{1}{n} \sum_{r=0}^{2 n-1} \frac{n^2}{n^2+4 r^2}\) is: [JEE Main 2021, 2…

Q1

The value of \(\lim _{n \rightarrow \infty} \frac{1}{n} \sum_{r=0}^{2 n-1} \frac{n^2}{n^2+4 r^2}\) is:

[JEE Main 2021, 26 Aug (Shift 1)]

a

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

b

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

c

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

d

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

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