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Sum the series tan^-1 frac{1}{1+1+1^2} +...

Sum the series `tan^-1 frac{1}{1+1+1^2} + tan^-1 frac{1}{1+2+2^2} + tan^-1 frac{1}{1+3+3^2} + …...... To oo`.

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tan^-1 frac{1}{2} + tan^-1 frac {2}{11} = tan^-1 frac{3}{4}

tan^-1 frac{2}{11} + tan^-1 frac {7}{24} = tan^-1 frac{1}{2}

tan^-1 frac{1}{2} + tan^-1 frac {1}{7} = tan^-1 frac{9}{13}

Prove that : 2 tan^-1 frac{1}{2} + tan^-1 frac{1}{7}=tan^-1 frac{31}{17}

tan^-1 frac{2}{11} + tan^-1 frac{7}{24}= frac{1}{2}cos^-1 frac{3}{5}

tan^-1 frac{1}{2} + tan^-1 frac{2}{11}= frac{1}{2}sin^-1 frac{24}{25}

Prove that : 2 tan^-1 frac{1}{7} + tan^-1 frac{1}{3}=tan^-1 frac{9}{13}

Prove that : 2 tan^-1 frac{1}{5} + tan^-1 frac{1}{8}= tan^-1 frac{4}{7}

Prove that : 2 tan^-1 frac{1}{5} + tan^-1 frac{1}{4}= tan^-1 frac{32}{43}

2tan^-1 frac{1}{3} + tan^-1 frac{1}{7}= frac {pi}{4}