Let \({S_k} = \sum\limits_{r = 1}^k {{{\tan }^{ - 1}}(\frac{{{6^r}}}{{{2^{2r + 1}} + {3^{2r + 1}}}}})\). Then \(\mathop {\lim }\limits_{k \to \infty } \) Sk is equal to:
1
\(\frac \pi 2\)
2
\(\rm{\cot ^{ - 1}}\left( {\frac{3}{2}} \right)\)
3
\(\rm{\tan ^{ - 1}}\left( {\frac{3}{2}} \right)\)
4
tan-1 (3)