query: Uniform convergence of the series $\sum_{n=1}^{\infty} \frac{1}{((x+\pi)n)^2}$ for $x \in (-\pi,\pi)$?
positive_passages.docid: 65312
positive_passages.text: Check the uniform convergence of series of functions
negative_passages.docid: 158737
negative_passages.text: What is the value of the series $\sum\limits_{n=1}^\infty \frac{(-1)^n}{n^2}$?
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: 105980
negative_passages.text: On convergence of Bertrand series $\sum\limits_{n=2}^{\infty} \frac{1}{n^{\alpha}\ln^{\beta}(n)}$ where $\alpha, \beta \in \mathbb{R}$
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: 5817
negative_passages.text: Does the series $\sum \limits_{n=2}^{\infty }\frac{n^{\log n}}{(\log n)^{n}}$ converge?
negative_passages.docid: 129078
negative_passages.text: Proving the series $\sum_{n=0}^{\infty}\sin(e\pi n!)$ converges
negative_passages.docid: 158741
negative_passages.text: Convergence of $\sum \frac{a_n}{(a_1+\ldots+a_n)^2}$
negative_passages.docid: 12480
negative_passages.text: Convergence of $\sum_{n=1}^{\infty} \frac{\frac{1}{2}+(-1)^n}{n}$
negative_passages.docid: 54730
negative_passages.text: For which $p$ does the series $\sum_{n=2}^{\infty} \frac{1}{(\log 1)^p+(\log 2)^p+\cdots +(\log n)^p}$ converge?
negative_passages.docid: 63380
negative_passages.text: Show that the series $\sum_{n=2}^{\infty} \frac{1}{n\, (\log n)^s}$ converges for $s >1$ and diverges for $s=1$
negative_passages.docid: 1098
negative_passages.text: Does $\sum\limits_{n=1}^\infty\frac{1}{\sqrt{n}+\sqrt{n+1}}$ converge?
negative_passages.docid: 112823
negative_passages.text: Convergence of the series $\sum_{1}^\infty \left(1-n\sin(\frac{1}{n})\right)$
negative_passages.docid: 117863
negative_passages.text: Series $\sum_{n=1}^\infty \frac{n^n}{(n!)^2}$
negative_passages.docid: 7041
negative_passages.text: Test for convergence of the series $\sum_{n=2}^\infty\frac{1}{(\ln n)^{\ln n}}$
negative_passages.docid: 27748
negative_passages.text: Convergence of $\sum \frac{a_n}{S_n ^{1 + \epsilon}}$ where $S_n = \sum_{i = 1} ^ n a_n$
negative_passages.docid: 129849
negative_passages.text: Convergence of the series $\sum_{n=1}^{\infty}\frac{e^n\,n!}{n^n}$