If S is the sum of the first 10 terms of the series ${\tan ^{ - 1}}\left( {{1 \over 3}} \right) + {\tan ^{ - 1}}\left( {{1 \over 7}} \right) + {\tan ^{ - 1}}\left( {{1 \over {13}}} \right) + {\tan ^{ - 1}}\left( {{1 \over {21}}} \right) + ....$ then tan(S) is equal to :

Question

If S is the sum of the first 10 terms of the series

${\tan ^{ - 1}}\left( {{1 \over 3}} \right) + {\tan ^{ - 1}}\left( {{1 \over 7}} \right) + {\tan ^{ - 1}}\left( {{1 \over {13}}} \right) + {\tan ^{ - 1}}\left( {{1 \over {21}}} \right) + ....$

then tan(S) is equal to :

${10 \over {11}}$

${5 \over {11}}$

-${6 \over {5}}$

${5 \over {6}}$

Solution

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