query: What is$\sum_{n=1}^\infty\frac{1}{n^2+1}$?
positive_passages.docid: 28378
positive_passages.text: Find the infinite sum of the series $\sum_{n=1}^\infty \frac{1}{n^2 +1}$
negative_passages.docid: 41751
negative_passages.text: $\sum_{n=1}^\infty \frac{i^n}{n}$ converge?
negative_passages.docid: 102581
negative_passages.text: Does $\sum_{n=1}^{\infty} \frac{1}{n^{1 + 1/n}}$ converge?
negative_passages.docid: 121554
negative_passages.text: Finding $\sum\frac{1}{2^n(n+1)}$
negative_passages.docid: 78473
negative_passages.text: Showing $ \sum_{n=0}^{\infty} \frac{1}{(3n+1)(3n+2)}=\frac{\pi}{3\sqrt{3}}$
negative_passages.docid: 62913
negative_passages.text: Understanding $\sum_{n=1}^{\infty} \frac{1}{n^4} = \frac{\pi^4}{90}$
negative_passages.docid: 127267
negative_passages.text: Evaluation of $\sum_{n=1}^{\infty}\frac{1}{n(2n+1)}=2-2\ln(2)$
negative_passages.docid: 150148
negative_passages.text: Sum of $\sum^\infty_{n=2} \frac{1}{\ln{(n!)}}$
negative_passages.docid: 63863
negative_passages.text: Evaluate: $\sum_{n=1}^{\infty}\frac{1}{n k^n}$
negative_passages.docid: 22636
negative_passages.text: Find the sum of the series $\sum \limits_{n=1}^{\infty} \frac{2^{-n}(n+3)}{(n+1)(n+2)}$
negative_passages.docid: 43903
negative_passages.text: Find the sum for $\sum_{n=1}^{\infty}(-1)^{(n+1)}\frac{2n+1}{3^n} $
negative_passages.docid: 137027
negative_passages.text: Find the value of $\sum_{n=0}^\infty\frac{1}{9n^2+9n+2}$
negative_passages.docid: 24373
negative_passages.text: Hint on computing the series $\sum_{n=2}^\infty \frac{1}{n^2-1}$.
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: 30407
negative_passages.text: Prove that $\sum_{n=1}^\infty\frac{n}{n^2+1}$ is divergent
negative_passages.docid: 135380
negative_passages.text: Show that $\sum_{n=1}^\infty \frac{n^2}{(n+1)!}=e-1$
negative_passages.docid: 25395
negative_passages.text: Sum $\sum_{n=1}^\infty \frac{n^2}{(n+2)!}$