JEE Math Practice Question

Let $${S_k} = \sum\limits_{r = 1}^k {{{\tan }^{ - 1}}\left( {{{{6^r}} \over {{2^{2r + 1}} + {3^{2r + 1}}}}} \right)} $$. Then $$\mathop {\lim }\limits_{k \to \infty } {S_k}$$ is equal to :

1. A.$${\cot ^{ - 1}}\left( {{3 \over 2}} \right)$$
2. B.$${\pi \over 2}$$
3. C.tan$$-$$1 (3)
4. D.$${\tan ^{ - 1}}\left( {{3 \over 2}} \right)$$