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The value of \(\lim _{n \rightarrow \infty} \sum_{k=1}^n \frac{n^3}{\left(n^2+k^2\right)\left(n^2+3 k^2\right)}\) is: [J…

Q1

The value of \(\lim _{n \rightarrow \infty} \sum_{k=1}^n \frac{n^3}{\left(n^2+k^2\right)\left(n^2+3 k^2\right)}\) is:

[JEE Main 2024, 30 Jan (Shift 1)]

a

\(\frac{13(2 \sqrt{3}-3) \pi}{8}\)

b

\(\frac{13 \pi}{8(4 \sqrt{3}+3)}\)

c

\(\frac{\pi}{8(2 \sqrt{3}+3)}\)

d

\(\frac{(2 \sqrt{3}+3) \pi}{24}\)

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