query: Test the convergence of the series $\sum \sin [\pi(\sqrt5+2)^n]$
positive_passages.docid: 148044
positive_passages.text: Does $\sum_{n=1}^{\infty} \sin(\pi(2+\sqrt{3})^n)$ converge? Converge absolutely?
negative_passages.docid: 137055
negative_passages.text: convergence or divergence of $\sum_{n=0}^∞ \frac{(\ln(n)+5)}{n^2}$
negative_passages.docid: 132613
negative_passages.text: Testing the series $\sum\limits_{n=1}^{\infty} \frac{1}{n^{k + \cos{n}}}$
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: 25762
negative_passages.text: How can I prove convergence of the series $\sum_{n=1}^{\infty}\frac{\log(n)}{n^2}$ by comparison?
negative_passages.docid: 52177
negative_passages.text: divergence/convergence $\sum_{k=1}^{\infty} \frac{1}{5k+2}$
negative_passages.docid: 30150
negative_passages.text: Testing convergence of series $\sum_{n=3}^\infty\frac{1}{n (\ln(n))^p(\ln\ln(n))^q}$
negative_passages.docid: 148389
negative_passages.text: Test the convergence of the series with alternating signs
negative_passages.docid: 155413
negative_passages.text: Testing the convergence of cube root of some function of n
negative_passages.docid: 135017
negative_passages.text: Test $f_n = (1+\frac{1}{n^2})^n$ for convergence and give its limit if it exists.
negative_passages.docid: 126264
negative_passages.text: Does the series $\sum \limits _{n=0}^{\infty} \cos(n\pi)$ converge or diverge?
negative_passages.docid: 129592
negative_passages.text: Prove the series $\sum_{n=1}^{\infty}\frac{1}{{5^n}^!}$ converges to an irrational number
negative_passages.docid: 62321
negative_passages.text: To test the convergence $\sum{\frac{1}{(\ln {n})^{\ln{n}}}}$
negative_passages.docid: 42742
negative_passages.text: Is $\sum_{n=1}^\infty \frac{\sin(2n)}{1+\cos^4(n)}$ convergent?
negative_passages.docid: 4220
negative_passages.text: Does $\int_{0}^{\infty}\frac{dx}{1+(x\sin5x)^2}$ converge?
negative_passages.docid: 25852
negative_passages.text: Does the series $\sum_{n=1}^\infty$ ${\sqrt{n+1}-\sqrt{n}}\over n$ converge or diverge?
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 $a_n>0$