query: Show that $\sum^{\infty}_{n=1}\frac{(-1)^n}{n}$ converges.
positive_passages.docid: 12812
positive_passages.text: Sum of the alternating harmonic series $\sum_{k=1}^{\infty}\frac{(-1)^{k+1}}{k} = \frac{1}{1} - \frac{1}{2} + \cdots $
negative_passages.docid: 71162
negative_passages.text: Showing that $\sum_{n=1}^{\infty} \frac{z^n}{1+z^{2n}}$ converges
negative_passages.docid: 2584
negative_passages.text: Convergence of an alternating series : $ \sum_{n\geq 1} \frac{(-1)^n|\sin n|}{n}$
negative_passages.docid: 44261
negative_passages.text: Convergence of $\sum^\infty_{n=1} \ln(1+\frac 1 {2^n})$
negative_passages.docid: 85285
negative_passages.text: Show $\sum_{i=1}^\infty x_i y_i$ is absolutely convergent
negative_passages.docid: 125341
negative_passages.text: Does $\sum_{n=1}^{\infty} \frac{1}{n+1}$ converge?
negative_passages.docid: 116046
negative_passages.text: Prove that if $\sum_{n=1}^\infty a_{2n}$ and $\sum_{n=1}^\infty a_{2n-1}$ converge then $\sum_{n=1}^\infty a_n$ converges.
negative_passages.docid: 38062
negative_passages.text: Proving the convergence of $\sum\limits_{n=1}^{\infty}\frac{1}{1+z^n}$ for $|z| > 1$
negative_passages.docid: 141200
negative_passages.text: How do I check the series $\sum_{n=2}^{\infty} \frac{(-1)^n }{n+(-1)^n}$ for absolute convergence/conditional convergence?
negative_passages.docid: 13979
negative_passages.text: Show that $\sum\limits_{n=0}^\infty \frac{z}{(1+z^2)^n}$ converges for all $z\in \mathbb{C}$ outside $|1+z^2|=1$
negative_passages.docid: 30439
negative_passages.text: Convergence of $\sum_{n=1}^{\infty}\frac{1}{n^\alpha}$
negative_passages.docid: 27153
negative_passages.text: Definition of convergence of $\sum_{i=-\infty}^\infty a_i$
negative_passages.docid: 48763
negative_passages.text: Convergence of $\sum_{n=1}^\infty \frac{\cos(n)}{n}$
negative_passages.docid: 27061
negative_passages.text: Is $\sum\limits_{n=1}^{\infty}\frac{n!}{n^n}$ convergent?
negative_passages.docid: 125340
negative_passages.text: Prove the convergence of a series.
negative_passages.docid: 100574
negative_passages.text: Convergence of $\sum_n \frac{n!}{n^n}$
negative_passages.docid: 140220
negative_passages.text: Convergence of $\sum_{n=2}^{\infty}\frac{\sqrt{a_{n}}}{\ln\, n}(n^{a_{n}}-1)$