query: What is the sum of $\arctan\frac{1}{2r^2}$
positive_passages.docid: 154172
positive_passages.text: Finding $\tan t$ if $t=\sum\tan^{-1}(1/2t^2)$
negative_passages.docid: 127806
negative_passages.text: How to find the sum of the series $\sum_{k=2}^\infty \frac{1}{k^2-1}$?
negative_passages.docid: 90030
negative_passages.text: What would be the value of $\sum\limits_{n=0}^\infty \frac{1}{an^2+bn+c}$
negative_passages.docid: 60288
negative_passages.text: Why is $\arctan(x)=x-x^3/3+x^5/5-x^7/7+\dots$?
negative_passages.docid: 49028
negative_passages.text: Find the sum : $\frac{1}{\cos0^\circ\cos1^\circ}+\frac{1}{\cos1^\circ \cos2^\circ} +\frac{1}{\cos2^\circ \cos3^\circ}+......+$
negative_passages.docid: 81589
negative_passages.text: Find the sum of $\sum_{k=0}^{\infty} 1/[(r+2k+2)(s+2k+2)]$
negative_passages.docid: 137249
negative_passages.text: find $\sum_{k=2}^{\infty}\frac{1}{k^2-1}$
negative_passages.docid: 36023
negative_passages.text: Showing that $ \sum_{n=1}^{\infty} \arctan \left( \frac{2}{n^2} \right) =\frac{3\pi}{4}$
negative_passages.docid: 153409
negative_passages.text: Sum of $1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{6}+\frac{1}{8}+\frac{1}{9}+\frac{1}{12}+\cdots$
negative_passages.docid: 35439
negative_passages.text: Does the series $\;\sum\limits_{n=0}^{\infty}\left(\frac{\pi}{2} - \arctan(n)\right)$ converge or diverge?
negative_passages.docid: 104453
negative_passages.text: A question about the arctangent addition formula.
negative_passages.docid: 100817
negative_passages.text: Generalizing $\int_{0}^{1} \frac{\arctan\sqrt{x^{2} + 2}}{\sqrt{x^{2} + 2}} \, \frac{\operatorname dx}{x^{2}+1} = \frac{5\pi^{2}}{96}$
negative_passages.docid: 100936
negative_passages.text: What is the sum of this series: $\frac{2}{\pi}\sum_{k=1}^{\infty}\frac{(-1)^{k-1}}{2k-1}$
negative_passages.docid: 65562
negative_passages.text: Proving the inequality $\arctan\frac{\pi}{2}\ge1$
negative_passages.docid: 106552
negative_passages.text: Find the sum of $\sum \frac{1}{k^2 - a^2}$ when $0<a<1$
negative_passages.docid: 103757
negative_passages.text: how can I prove that $\frac{\arctan x}{x }< 1$?
negative_passages.docid: 46706
negative_passages.text: Integral $\int_0^2 \frac{\arctan x}{x^2+2x+2}dx$