query: Convergence $I=\int_0^\infty \frac{\sin x}{x^s}dx$
positive_passages.docid: 22109
positive_passages.text: Convergence of $\int_0^\infty \sin(t)/t^\gamma \mathrm{d}t$
negative_passages.docid: 14050
negative_passages.text: Determining precisely where $\sum_{n=1}^\infty\frac{z^n}{n}$ converges?
negative_passages.docid: 9921
negative_passages.text: Convergence of $\sum_{n=1}^\infty\frac{n}{(n+1)!}$
negative_passages.docid: 147930
negative_passages.text: Does $\sum_{n=1}^{\infty}\frac {\sin{\frac 1 n}} {\sqrt n}$ converge?
negative_passages.docid: 69348
negative_passages.text: Prove that $\int \limits _{0}^{\infty}\frac{e^{-2x}-e^{-ax}}{x}\text{d}x$ converges for any $a>0$
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: 150458
negative_passages.text: Interval of convergence of $\sum_{n=0}^\infty (\frac{n}{n+1})^{n^2}(2x)^n$
negative_passages.docid: 59427
negative_passages.text: convergence to infinity of$ (2^n + 3^n)^{\frac{1}{n}}$ (as $n \to \infty$)
negative_passages.docid: 23368
negative_passages.text: Does $\int_1^2\frac{\sin{x}}{\log{x}} \, dx$ converge?
negative_passages.docid: 48763
negative_passages.text: Convergence of $\sum_{n=1}^\infty \frac{\cos(n)}{n}$
negative_passages.docid: 117583
negative_passages.text: Why does $\sum_{n=0}^\infty (\sin{\frac{1}{n}})(\sinh{\frac{1}{n}})(\cos n)$ converge
negative_passages.docid: 27323
negative_passages.text: Convergence of the complex series $\sum_{n=0}^{\infty} \frac{(-1)^{n}}{z+n}$
negative_passages.docid: 110055
negative_passages.text: Convergence of the series $\sum_{n=1}^{\infty}((1/n)-\sin(1/n))$..?
negative_passages.docid: 135110
negative_passages.text: Pointwise convergence of $h_n(x) = x^{1+\frac{1}{2n-1}}$
negative_passages.docid: 10547
negative_passages.text: $\int_0^\infty \frac{\sin(x^2+ax)}{x}\,dx$ converges
negative_passages.docid: 59667
negative_passages.text: Evaluating $\int_0^\infty\frac{\sin(x)}{x^2+1}\, dx$
negative_passages.docid: 63612
negative_passages.text: Determine convergence of $\sum_{n=1}^{\infty}a_n$