defence exam Agniveer Vayu Group X & XY Mock Test 01/2026 Mathematics Limit and Continuity Evaluation of Limits
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:
1
\(\frac{(2 \sqrt{3}+3) \pi}{24}\)
2
\(\frac{13 \pi}{8(4 \sqrt{3}+3)}\)
3
\(\frac{13(2 \sqrt{3}-3) \pi}{8}\)
4
\(\frac{\pi}{8(2 \sqrt{3}+3)}\)