Let S_k =Σ_r =1^k tan^-1((6^r)/(2^2 r +1 +3^2 r +1)). Then lim_k → ∞ S_k is equal to:

Let $\displaystyle \mathrm{S}_{\mathrm{k}}=\sum_{\mathrm{r}=1}^{\mathrm{k}} \tan ^{-1}\left(\frac{6^{\mathrm{r}}}{2^{2 \mathrm{r}+1}+3^{2 \mathrm{r}+1}}\right)$. Then $\displaystyle \lim _{\mathrm{k} \rightarrow \infty} \mathrm{S}_{\mathrm{k}}$ is equal to :