JEE Math Practice Question
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 :
- A.$$\frac{\pi}{8(2 \sqrt{3}+3)}$$
- B.$$\frac{(2 \sqrt{3}+3) \pi}{24}$$
- C.$$\frac{13 \pi}{8(4 \sqrt{3}+3)}$$
- D.$$\frac{13(2 \sqrt{3}-3) \pi}{8}$$
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