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 :

Question

${\cot ^{ - 1}}\left( {{3 \over 2}} \right)$

${\pi \over 2}$

tan^$-$1 (3)

${\tan ^{ - 1}}\left( {{3 \over 2}} \right)$

Solution

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