query: Does the series $\sum_{1}^{\infty}\big[1 + n\ln\big(\frac{2n-1}{2n+1}\big) \big]$ converge?
positive_passages.docid: 43576
positive_passages.text: Convergence of $\sum _{n=1}^{\infty }\left\{ 1-n\log \frac {2n+1} {2n-1}\right\} $
negative_passages.docid: 123108
negative_passages.text: Does the series $ \sum\limits_{n=1}^{\infty} \frac{1}{n^{1 + |\sin(n)|}} $ converge or diverge?
negative_passages.docid: 65939
negative_passages.text: Is this convergent or divergent: $\sum _{n=1}^{\infty }\:\frac{2n^2}{5n^2+2n+1}$?
negative_passages.docid: 127267
negative_passages.text: Evaluation of $\sum_{n=1}^{\infty}\frac{1}{n(2n+1)}=2-2\ln(2)$
negative_passages.docid: 158703
negative_passages.text: Is series $\sum_{n=1}^{\infty}\frac{\cos(nx)}{n^\alpha}$, for $\alpha>0$, convergent?
negative_passages.docid: 78167
negative_passages.text: Show that the series $\sum\limits_{n=2}^{\infty} \frac {(n^3+1)^{1/3}-n}{\log n}$ converges
negative_passages.docid: 125933
negative_passages.text: On the series $\sum \limits_{n=2}^{\infty} \frac{(-1)^n}{n \log n}$
negative_passages.docid: 77183
negative_passages.text: Prove that $ \sum_{n=1}^\infty \ln\big(n\sin \frac{1}{n}\big)$ converges.
negative_passages.docid: 129849
negative_passages.text: Convergence of the series $\sum_{n=1}^{\infty}\frac{e^n\,n!}{n^n}$
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: 47980
negative_passages.text: Infinite series $\sum _{n=2}^{\infty } \frac{1}{n \log (n)}$
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: 37802
negative_passages.text: Why doesn't $\sum_{n=1}^\infty \frac{1}{n^{1+\frac{1}{n}}}$ converge?
negative_passages.docid: 95353
negative_passages.text: Does $\sum_{n=1}^\infty \frac{\cos{(\sqrt{n})}}{n}$ converge?
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: 102581
negative_passages.text: Does $\sum_{n=1}^{\infty} \frac{1}{n^{1 + 1/n}}$ converge?
negative_passages.docid: 40698
negative_passages.text: Does the series $\sum\limits_{n=1}^\infty \frac{1}{n^3 \sin^2n}$ converge or diverge?