Infinite Tangent....

Geometry Level 4

Let \[S=\tan^{ -1 }{ \frac { 1 }{ 2\times 1 } }+\tan^{ -1 }{ \frac { 1 }{ 2\times 4 } }+\tan^{ -1 }{ \frac { 1 }{ 2\times 9 } }+....upto\quad\infty \] Find the value of \(\frac { \pi }{ S } \)

DETAILS

\(\arctan { x } =\tan ^{ -1 }{ x } \neq \frac { 1 }{ \tan { x } } \)

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