query: Convergence of the series $\sum_{n\geq 2}\text{log}(1+\frac{(-1)^n}{\sqrt{n}})$
positive_passages.docid: 27260
positive_passages.text: Infinite product with sign changes.
negative_passages.docid: 12480
negative_passages.text: Convergence of $\sum_{n=1}^{\infty} \frac{\frac{1}{2}+(-1)^n}{n}$
negative_passages.docid: 19159
negative_passages.text: Convergence of $\frac{1}{(\ln n)^{\ln n}}$
negative_passages.docid: 65249
negative_passages.text: An interesting exercise about converging positive series, involving $\sum_{n\geq 1}a_n^{\frac{n-1}{n}}$
negative_passages.docid: 32964
negative_passages.text: Convergence of $\sum \frac{\sqrt{a_n}}{n^p}$
negative_passages.docid: 100574
negative_passages.text: Convergence of $\sum_n \frac{n!}{n^n}$
negative_passages.docid: 9044
negative_passages.text: Convergence of the sequence $(1+\frac{1}{n})(1+\frac{2}{n})\cdots(1+\frac{n}{n})$
negative_passages.docid: 44261
negative_passages.text: Convergence of $\sum^\infty_{n=1} \ln(1+\frac 1 {2^n})$
negative_passages.docid: 32423
negative_passages.text: Convergence of $\sum _{k=1}^\infty (1-\frac{1}{k})^{k^2}$
negative_passages.docid: 125933
negative_passages.text: On the series $\sum \limits_{n=2}^{\infty} \frac{(-1)^n}{n \log n}$
negative_passages.docid: 79415
negative_passages.text: The series $\sum_{n=2}^{\infty }\frac{1}{\log (n!)}$
negative_passages.docid: 34736
negative_passages.text: Convergence of series involving in iterated logarithms $\sum \frac{1}{n(\log n)^{\alpha_1}\cdots (\log^k(n))^{\alpha_k} }$
negative_passages.docid: 134576
negative_passages.text: Does this series converge or diverge? $\sum_{n=1}^\infty\ln\left(1+\frac1{n^2}\right)$
negative_passages.docid: 89373
negative_passages.text: Convergence of $\frac{\sqrt{a_{n}}}{n}$
negative_passages.docid: 54376
negative_passages.text: Convergence of the series $\sqrt[n]n-1$
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: 48763
negative_passages.text: Convergence of $\sum_{n=1}^\infty \frac{\cos(n)}{n}$