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

Question

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

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

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

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

Please login to view the detailed solution steps...