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$\mathop {\lim }\limits_{x \to \infty } \,\left( {\frac{n}{{{n^2}\, + {1^2}}} + \frac{n}{{{n^2} + {2^2}}} + \frac{n}{{{n^2} + {3^2}}} + ...\frac{1}{{5n}}} \right)$ is equal to

• A
  $\frac{\pi }{4}$
• B
  $tan^{-1}\,\,(3)$
• C
  $\frac{\pi }{2}$
• ✓
  $tan^{-1}\,\,(2)$