query: Evaluating $\sum_{n=1}^{\infty} \frac{\left(\frac{1}{2}\right)^n}{n^2}$
positive_passages.docid: 18518
positive_passages.text: Proof of dilogarithm reflection formula $\zeta(2)-\log(x)\log(1-x)=\operatorname{Li}_2(x)+\operatorname{Li}_2(1-x)$
negative_passages.docid: 133955
negative_passages.text: Compute: $\sum_{k=1}^{\infty}\sum_{n=1}^{\infty} \frac{1}{k^2n+2nk+n^2k}$
negative_passages.docid: 8705
negative_passages.text: Evaluation of $\sum_{x=0}^\infty e^{-x^2}$
negative_passages.docid: 91784
negative_passages.text: Calculating $\sum_{n=1}^\infty {\frac{1}{2^nn(3n-1)}}$
negative_passages.docid: 62443
negative_passages.text: Prove that $\sum_{n=1}^\infty \ln\left(\frac{n(n+2)}{(n+1)^2}\right)$ converges and find its sum
negative_passages.docid: 117370
negative_passages.text: $\lim_{n\to\infty} \left(1+\frac{2}{n}\right)^{n^2} e^{-2n}$
negative_passages.docid: 56961
negative_passages.text: Evaluate the limit of $\sum_{n=1}^{\infty}\frac{n^2}{n!}$
negative_passages.docid: 56365
negative_passages.text: Evaluate $\sum\limits_{k=1}^{n} \frac{k}{2^k}$
negative_passages.docid: 135380
negative_passages.text: Show that $\sum_{n=1}^\infty \frac{n^2}{(n+1)!}=e-1$
negative_passages.docid: 125497
negative_passages.text: Evaluating $\lim_{n \to \infty} n\left(1-\frac{1}{e}\left(1+\frac{1}{n}\right)^{n} \right)$
negative_passages.docid: 142218
negative_passages.text: $\sum_{n=1}^{\infty}\frac{1}{n^22^n}$ by integration or differentiation
negative_passages.docid: 152698
negative_passages.text: Evaluation of $\sum_{n=0}^{\infty}\frac{1}{(n^4+n^2+1)n!}$
negative_passages.docid: 104365
negative_passages.text: Evaluate: $\lim_{n\to\infty}\left({2\sqrt n}-\sum_{k=1}^n\frac1{\sqrt k}\right)$
negative_passages.docid: 82831
negative_passages.text: Evaluating the limit $\lim_{n\to\infty} \left[ \frac{n}{n^2+1}+ \frac{n}{n^2+2^2} + \ldots + \frac{n}{n^2+n^2} \right]$
negative_passages.docid: 47572
negative_passages.text: Evaluate $ \sum_{n=1}^{\infty} \frac{\sin \ n}{ n } $ using the fourier series
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: 37007
negative_passages.text: Evaluating $\sum_{k=1}^{n} \frac{1}{k(k+1)}$