query: Determine if $ \intop_{0}^{\infty}\frac{dx}{1+\left(x\sin5x\right)^{2}} $ converge
positive_passages.docid: 4220
positive_passages.text: Does $\int_{0}^{\infty}\frac{dx}{1+(x\sin5x)^2}$ converge?
negative_passages.docid: 76050
negative_passages.text: Test for convergence of the series $\sum_{n=1}^{\infty}\frac{n}{\sqrt{n^2 +1}}$
negative_passages.docid: 145335
negative_passages.text: Is $ \int_0^1{\frac{\sin x}{x}dx} $ convergent?
negative_passages.docid: 22109
negative_passages.text: Convergence of $\int_0^\infty \sin(t)/t^\gamma \mathrm{d}t$
negative_passages.docid: 30150
negative_passages.text: Testing convergence of series $\sum_{n=3}^\infty\frac{1}{n (\ln(n))^p(\ln\ln(n))^q}$
negative_passages.docid: 16970
negative_passages.text: Convergence of $\sqrt{n}x_{n}$ where $x_{n+1} = \sin(x_{n})$
negative_passages.docid: 74903
negative_passages.text: Find out whether $\sum_{k=1}^{\infty}\left(\frac{1+\cos k}{2+\cos k}\right)^{2k}$ converges absolutely, conditionally or diverges.
negative_passages.docid: 149360
negative_passages.text: convergence of $ \sum_{k=1}^\infty \sin^2(\frac 1 k)$
negative_passages.docid: 26370
negative_passages.text: Consider convergence of series: $\sum_{n=1}^{\infty}\sin\left[\pi\left(2+\sqrt{3}\right)^n\right]$
negative_passages.docid: 150458
negative_passages.text: Interval of convergence of $\sum_{n=0}^\infty (\frac{n}{n+1})^{n^2}(2x)^n$
negative_passages.docid: 94792
negative_passages.text: Convergence of a series $\sum\limits_{n=1}^\infty\left(\frac{a_n}{n^p}\right)^\frac{1}{2}$
negative_passages.docid: 43576
negative_passages.text: Convergence of $\sum _{n=1}^{\infty }\left\{ 1-n\log \frac {2n+1} {2n-1}\right\} $
negative_passages.docid: 61647
negative_passages.text: Determine when $\sum_1^\infty \frac{(2n)!x^n}{n(n!)^2}$ converges.
negative_passages.docid: 121971
negative_passages.text: How to test the convergence for $\sum _{n=3}^{\infty }\:\left(-\frac{1}{\sqrt{ln\left(n\right)}}\right)^{n+1}$?
negative_passages.docid: 102581
negative_passages.text: Does $\sum_{n=1}^{\infty} \frac{1}{n^{1 + 1/n}}$ converge?
negative_passages.docid: 112772
negative_passages.text: Is the series $\sum \limits_{n=1}^{\infty} \sin(n^2)$ convergent?
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 $|1+z^2|=1$