query: Find the sum of he series to infinity : $\tan^{-1} (\frac 12) + \tan^{-1} (\frac 18) + \tan^{-1} (\frac{1}{18})...$
positive_passages.docid: 156720
positive_passages.text: Evaluate $\sum_ {n=1}^{\infty} \cot^{-1}(2n^2)$
negative_passages.docid: 57759
negative_passages.text: Determining the infinite sum $\sum\limits_{n=0}^{\infty}\frac{(-1)^n}{2n+1}$
negative_passages.docid: 52987
negative_passages.text: $\sum_{n=-\infty}^{\infty}\frac{1}{(n+\alpha)^2}=\frac{\pi^2}{(\sin \pi \alpha)^2}$?
negative_passages.docid: 139221
negative_passages.text: Compute the series $\sum_{n=1}^{+\infty} \frac{1}{n^3\sin(n\pi\sqrt{2})}.$
negative_passages.docid: 89771
negative_passages.text: $\frac{1}{s-1}+\sum_{n=1}^{\infty}\left[\frac{1}{n^s}+\frac{1}{s-1}\left(\frac{1}{(n+1)^{s-1}} - \frac{1}{n^{s-1}}\right)\right]$
negative_passages.docid: 9960
negative_passages.text: Sum of an infinite series $(1 - \frac 12) + (\frac 12 - \frac 13) + \cdots$ - not geometric series?
negative_passages.docid: 122445
negative_passages.text: Sum of the series:$\frac{1}{1\cdot 2}+\frac{1\cdot3}{1\cdot2\cdot3\cdot4}+\cdots$
negative_passages.docid: 148883
negative_passages.text: Sum of the series $\frac{1}{2\cdot 4}+\frac{1\cdot3}{2\cdot4\cdot6}+\dots$
negative_passages.docid: 93837
negative_passages.text: How to compute infinite series $\sum_{n=0}^{\infty} ne^{-n}$
negative_passages.docid: 32866
negative_passages.text: How find this sum $\sum\limits_{n=0}^{\infty}\frac{1}{(3n+1)(3n+2)(3n+3)}$
negative_passages.docid: 130548
negative_passages.text: What is the sum of the power series: $\sum_{k=2}^\infty\frac{x^k}{k(k-1)}$?
negative_passages.docid: 62271
negative_passages.text: Find the sum of the series: $\cos^3 \alpha +\cos^3 {3\alpha} + \cos^3 {5\alpha}+....+\cos^3 {(2n-1)\alpha}$.
negative_passages.docid: 148143
negative_passages.text: Find the sum to n terms as well as the sum to infinity of the series:
negative_passages.docid: 91784
negative_passages.text: Calculating $\sum_{n=1}^\infty {\frac{1}{2^nn(3n-1)}}$
negative_passages.docid: 158737
negative_passages.text: What is the value of the series $\sum\limits_{n=1}^\infty \frac{(-1)^n}{n^2}$?
negative_passages.docid: 92690
negative_passages.text: Infinite Series $\sum\limits_{n=0}^{\infty}\arctan(\frac{1}{F_{2n+1}})$
negative_passages.docid: 154172
negative_passages.text: Finding $\tan t$ if $t=\sum\tan^{-1}(1/2t^2)$