jee-main 2021 Q71

jee-main · India · session2_16mar_shift1 Standard trigonometric equations Inverse trigonometric equation

Let $S _ { k } = \sum _ { r = 1 } ^ { k } \tan ^ { - 1 } \left( \frac { 6 ^ { r } } { 2 ^ { 2 r + 1 } + 3 ^ { 2 r + 1 } } \right)$, then $\lim _ { k \rightarrow \infty } S _ { k }$ is equal to :
(1) $\tan ^ { - 1 } \left( \frac { 3 } { 2 } \right)$
(2) $\frac { \pi } { 2 }$
(3) $\cot ^ { - 1 } \left( \frac { 3 } { 2 } \right)$
(4) $\tan ^ { - 1 } ( 3 )$

Let $S _ { k } = \sum _ { r = 1 } ^ { k } \tan ^ { - 1 } \left( \frac { 6 ^ { r } } { 2 ^ { 2 r + 1 } + 3 ^ { 2 r + 1 } } \right)$, then $\lim _ { k \rightarrow \infty } S _ { k }$ is equal to :\\
(1) $\tan ^ { - 1 } \left( \frac { 3 } { 2 } \right)$\\
(2) $\frac { \pi } { 2 }$\\
(3) $\cot ^ { - 1 } \left( \frac { 3 } { 2 } \right)$\\
(4) $\tan ^ { - 1 } ( 3 )$

Paper Questions

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