query: convergence of $\sum_{n=1}^{\infty }\frac{(-1)^{[\sqrt{n}]}}{n}$ where $[a]$ means floor function of $a$
positive_passages.docid: 152802
positive_passages.text: How find series $\sum_{n=1}^{\infty}\frac{(-1)^{[\sqrt[m]{n}]}}{n^a}$?
negative_passages.docid: 27061
negative_passages.text: Is $\sum\limits_{n=1}^{\infty}\frac{n!}{n^n}$ convergent?
negative_passages.docid: 150000
negative_passages.text: Convergence of the sequence $\frac{1}{n\sin(n)}$
negative_passages.docid: 36243
negative_passages.text: Several ways to prove that $\sum\limits^\infty_{n=1}\left(1-\frac1{\sqrt{n}}\right)^n$ converges
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: 32423
negative_passages.text: Convergence of $\sum _{k=1}^\infty (1-\frac{1}{k})^{k^2}$
negative_passages.docid: 48763
negative_passages.text: Convergence of $\sum_{n=1}^\infty \frac{\cos(n)}{n}$
negative_passages.docid: 162
negative_passages.text: Determine the convergence of $ \sum_{n=1}^{\infty}\left[1-\cos\left(1 \over n\right)\right] $
negative_passages.docid: 91009
negative_passages.text: Convergence of the series $\sum a_n$ implies the convergence of $\sum \frac{\sqrt a_n}{n}$, if $a_n>0$
negative_passages.docid: 76867
negative_passages.text: Does $\sum _{k=2} ^\infty \frac{(-1)^k}{\sqrt{k}+(-1)^k}$ converge conditionally?
negative_passages.docid: 57372
negative_passages.text: Series convergence of $\sum_{n=1}^{\infty}\frac{1}{n^3}$
negative_passages.docid: 25503
negative_passages.text: Convergence of $\sum_{n=1}^\infty \frac{\sin^2(n)}{n}$
negative_passages.docid: 127627
negative_passages.text: Does $\sum^{\infty}_{n=1} n/(n-1)!$ converge to something?
negative_passages.docid: 85268
negative_passages.text: Convergence of $\sum_{n=1}^{\infty}{\sqrt[n]{n}-1 \over n}$
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: 30439
negative_passages.text: Convergence of $\sum_{n=1}^{\infty}\frac{1}{n^\alpha}$
negative_passages.docid: 126656
negative_passages.text: Convergence or divergence of $\sum\limits_n(-1)^{\pi(n)}\frac1n$ where $\pi(n)$ is the number of primes less than or equal to $n$