The value of lim_n→∞ (Σ_(k=1)ⁿ n³/(n²+k²)(n²+3k²)) is: | JEE Main 2024 Mathematics PYQ | Jeeify

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MCQMediumJEE Main 2024 · 30 January, Shift 1Definite Integrals

The value of $\lim_{n\to\infty} \left(\sum_{k=1}^{n} \frac{n^3}{(n^2+k^2)(n^2+3k^2)}\right)$ is:

A
$\frac{(2\sqrt{3}+3)\pi}{24}$
B
$\frac{13\pi}{8(4\sqrt{3}+3)}$
C
$\frac{13(2\sqrt{3}-3)\pi}{8}$
D
$\frac{\pi}{8(2\sqrt{3}+3)}$

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