query: $\sum_1^n 2\sqrt{n} - \sqrt{n-1} - \sqrt{n+1} $ converge or not?
positive_passages.docid: 17902
positive_passages.text: Prove or disprove: $\sum a_n$ convergent, where $a_n=2\sqrt{n}-\sqrt{n-1}-\sqrt{n+1}$.
negative_passages.docid: 63900
negative_passages.text: Convergent or divergent series: $\sum_{n=1}^{\infty} \sqrt{a_n \cdot a_{n+1}}$?
negative_passages.docid: 27068
negative_passages.text: Show that $\sqrt{2+\sqrt{2+\sqrt{2...}}}$ converges to 2
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: 76050
negative_passages.text: Test for convergence of the series $\sum_{n=1}^{\infty}\frac{n}{\sqrt{n^2 +1}}$
negative_passages.docid: 9921
negative_passages.text: Convergence of $\sum_{n=1}^\infty\frac{n}{(n+1)!}$
negative_passages.docid: 85268
negative_passages.text: Convergence of $\sum_{n=1}^{\infty}{\sqrt[n]{n}-1 \over n}$
negative_passages.docid: 112772
negative_passages.text: Is the series $\sum \limits_{n=1}^{\infty} \sin(n^2)$ convergent?
negative_passages.docid: 137997
negative_passages.text: Does the series $\sum \frac{x^n}{1+x^n}$ converge uniformly on $x\in [0,1)$?
negative_passages.docid: 35929
negative_passages.text: Convergence of series $\sum_{n=1}^{\infty}{\frac{1}{\sqrt{1}+\sqrt{2}+...+\sqrt{n}}}$
negative_passages.docid: 68404
negative_passages.text: Check whether $\sum _{m=1}^{\infty }\sum _{n=1}^{\infty }\frac{1}{\left(m+n\right)^2}$ converges or NOT?
negative_passages.docid: 41751
negative_passages.text: $\sum_{n=1}^\infty \frac{i^n}{n}$ converge?
negative_passages.docid: 131518
negative_passages.text: Test for convergence $\sum_{n=1}^{\infty}\{(n^3+1)^{1/3} - n\}$
negative_passages.docid: 140220
negative_passages.text: Convergence of $\sum_{n=2}^{\infty}\frac{\sqrt{a_{n}}}{\ln\, n}(n^{a_{n}}-1)$
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: 138516
negative_passages.text: $\sum (-1)^{n+1}\log\left(1+\frac{1}{n}\right)$ convergent but not absolutely convergent
negative_passages.docid: 122413
negative_passages.text: Show $b_n=\sqrt[k]{n+1}-\sqrt[k]{n}$ converges towards $0$ for all $k \geq 2$.