query: The sum $\sum_{k=1}^{\infty}(-1)^k \frac {\log(2k+1)}{(2k+1)}$
positive_passages.docid: 20471
positive_passages.text: Evaluating a slow sum
negative_passages.docid: 107789
negative_passages.text: Sum of $\sum \limits_{n=0}^{\infty} \frac{1}{(kn)!}$
negative_passages.docid: 21142
negative_passages.text: $\sum_{k=0} ^\infty (-1)^k \frac{(2k)!!}{(2k+1)!!} a^{2k+1}$ to differential equation
negative_passages.docid: 24373
negative_passages.text: Hint on computing the series $\sum_{n=2}^\infty \frac{1}{n^2-1}$.
negative_passages.docid: 150563
negative_passages.text: Find the sum $\sum_{n=1}^{\infty} \frac{\ln n}{n(n- \ln n)}$
negative_passages.docid: 101052
negative_passages.text: Find the infinite sum $\sum_{k=1}^{\infty}\sqrt k - 2\sqrt {k + 1} + \sqrt {k + 2} $
negative_passages.docid: 92810
negative_passages.text: What is $\sum_{r=1}^\infty\frac{r+2}{2^{r+1}(r)(r+1)}$?
negative_passages.docid: 106028
negative_passages.text: Sum of $\frac{1}{(2n)(2n+1)}$ from $1$ to infinity
negative_passages.docid: 6436
negative_passages.text: Proving an alternating Euler sum: $\sum_{k=1}^{\infty} \frac{(-1)^{k+1} H_k}{k} = \frac{1}{2} \zeta(2) - \frac{1}{2} \log^2 2$
negative_passages.docid: 59253
negative_passages.text: Summing the power series $\sum\limits_{n=0}^\infty (-1)^n \frac{x^{2n+1}}{2n+1}\prod\limits_{k=1}^n\frac{2k-1}{2k} $
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: 134152
negative_passages.text: Prove $\sum_{n=1}^\infty(e-\sum_{k=0}^n\frac1{k!})=1$
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: 19899
negative_passages.text: infinite series of the form $\sum\limits_{k=1}^{\infty}\frac{1}{a^{k}+1}$
negative_passages.docid: 99420
negative_passages.text: Compute $\sum_{n=1}^\infty \frac{1}{(n+1)\sqrt[]{n}+n\sqrt[]{n+1}}$
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: 127189
negative_passages.text: sum of this series: $\sum_{n=1}^{\infty}\frac{1}{4n^2-1}$