the value of 2 cot(cot^(-1)(3)+cot^(-1)(7)+cot^(-1)(13)+ cot^(-1)(21)) is

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c o t^{- 1} 3 + c o t^{- 1} 7 + c o t^{- 1} 13 + c o t^{- 1} 21 + . . . . . .

Sum of first n terms in the following series

${c o t}^{- 1}$ 3 + ${c o t}^{- 1}$ 7 + ${c o t}^{- 1}$ 13 + ${c o t}^{- 1}$ 21 + .........n terms.is given by

c o t^{- 1} 3 + c o t^{- 1} 7 + c o t^{- 1} 13 + . . . .

\cot^{- 1} \frac{1}{\sqrt{3}} - {cosec}^{- 1} (- 2) + \sec^{- 1} (\frac{2}{\sqrt{3}})

\cot^{- 1} \{2 \cos (\sin^{- 1} \frac{\sqrt{3}}{2})\}

{cosec}^{- 1} (- \frac{2}{\sqrt{3}}) + 2 \cot^{- 1} (- 1)

\tan^{- 1} (- \frac{1}{\sqrt{3}}) + \cot^{- 1} (\frac{1}{\sqrt{3}}) + \tan^{- 1} (\sin (- \frac{π}{2}))

2 cot ({cot}^{- 1} (3) + {cot}^{- 1} (7) + {cot}^{- 1} (13) + {cot}^{- 1} (21))

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