query: Is $(\frac 1{n^2 \sin n })$ convergent ? If so , what is the limit?
positive_passages.docid: 40867
positive_passages.text: Are there any series whose convergence is unknown?
negative_passages.docid: 113585
negative_passages.text: Does $\sum\limits_{k=1}^∞\frac1{k^{\ln k}}$ converge or diverge?
negative_passages.docid: 70867
negative_passages.text: Is $\sum_{n=1}^\infty\frac{(-1)^n}{n\log^2(n+1)}$ absolutely convergent?
negative_passages.docid: 35439
negative_passages.text: Does the series $\;\sum\limits_{n=0}^{\infty}\left(\frac{\pi}{2} - \arctan(n)\right)$ converge or diverge?
negative_passages.docid: 12480
negative_passages.text: Convergence of $\sum_{n=1}^{\infty} \frac{\frac{1}{2}+(-1)^n}{n}$
negative_passages.docid: 102581
negative_passages.text: Does $\sum_{n=1}^{\infty} \frac{1}{n^{1 + 1/n}}$ converge?
negative_passages.docid: 89373
negative_passages.text: Convergence of $\frac{\sqrt{a_{n}}}{n}$
negative_passages.docid: 129823
negative_passages.text: Show that $\sum_{n=1}^{\infty}(n^{3}\sin\left(\frac{1}{n}\right)-n^{2}+\frac{1}{6})$ converges
negative_passages.docid: 90106
negative_passages.text: Why this :$\sum\limits_{n=1}^\infty\frac1{n\sin n}$ is not harmonic series and is convergent?
negative_passages.docid: 100574
negative_passages.text: Convergence of $\sum_n \frac{n!}{n^n}$
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: 7881
negative_passages.text: For what values of $a$ does $\sum_{n=1}^\infty \left( 1+\frac12 + \dotsb + \frac1n \right) \frac{\sin (na)}{n}$ converge?
negative_passages.docid: 44288
negative_passages.text: Is my proof of convergence for $\sum\limits^{\infty}_{n=1} \frac {2^n} {n^n}$ true?
negative_passages.docid: 135565
negative_passages.text: Limit of $\frac{1}{x^2}-\frac{1}{\sin^2(x)}$ as $x$ approaches $0$
negative_passages.docid: 65362
negative_passages.text: Does $\sum{\frac{\sin{(nx)}}{n}}$ converge uniformly for all $x$ in $[0,2\pi]$
negative_passages.docid: 10547
negative_passages.text: $\int_0^\infty \frac{\sin(x^2+ax)}{x}\,dx$ converges
negative_passages.docid: 16642
negative_passages.text: Showing $a_n=\sin(n)$ does not converge