Tan−1(13)+ Tan−1(29)+ Tan−1(433)+ ...Infinite terms

Tn=tan−1(2n−11+ 22n−1) =tan−1(2n−2n−11+ 2n. 2n−1)=tan−12n−tan−1 2n−1 S∞ =∑n=1∞Tn=tan−1∞−tan−11

Tan−1(13)+ Tan−1(29)+ Tan−1(433)+ ...Infinite terms

Tn=tan−1(2n−11+ 22n−1) =tan−1(2n−2n−11+ 2n. 2n−1)=tan−12n−tan−1 2n−1 S∞ =∑n=1∞Tn=tan−1∞−tan−11

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$T a n^{- 1} (\frac{1}{3}) + T a n^{- 1} (\frac{2}{9}) + T a n^{- 1} (\frac{4}{33}) + ... Infinite terms$

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$T_{n} = \tan^{- 1} (\frac{2^{n - 1}}{1 + 2^{2 n - 1}}) = \tan^{- 1} (\frac{2^{n} - 2^{n - 1}}{1 + 2^{n} . 2^{n - 1}}) = \tan^{- 1} 2^{n} - \tan^{- 1} 2^{n - 1} S_{\infty} = \sum_{n = 1}^{\infty} T_{n} = \tan^{- 1} \infty - \tan^{- 1} 1$

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Tan−1(13)+ Tan−1(29)+ Tan−1(433)+ ...Infinite terms

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$T a n^{- 1} (\frac{1}{3}) + T a n^{- 1} (\frac{2}{9}) + T a n^{- 1} (\frac{4}{33}) + ... Infinite terms$