query: Determine the convergence of $\sum_{n=1}^\infty \frac{4^n+n}{n!}$
positive_passages.docid: 23215
positive_passages.text: Use any method, determine whether the series $\sum_{k=1}^{\infty} \frac{7^{k} + k}{k! + 1}$ converges?
negative_passages.docid: 91045
negative_passages.text: Converge or diverge? : $\sum_{n=1}^{\infty}\frac{\tan{n}}{2^{n}}$
negative_passages.docid: 19865
negative_passages.text: Convergence/Divergence of infinite series $\sum_{n=1}^{\infty} \frac{(\sin n+2)^n}{n3^n}$
negative_passages.docid: 154042
negative_passages.text: Discuss convergence of the series $\sum \frac{(1+n)^n}{n!}x^n$.
negative_passages.docid: 125341
negative_passages.text: Does $\sum_{n=1}^{\infty} \frac{1}{n+1}$ converge?
negative_passages.docid: 33965
negative_passages.text: Convergence of $\sum_{n=1}^\infty (-1)^n(\sqrt{n+1}-\sqrt n)$
negative_passages.docid: 97007
negative_passages.text: Does $\sum_{m=0}^{\infty} {2m\choose m} \frac{1}{4^{m}} $ converge?
negative_passages.docid: 9662
negative_passages.text: For what real values of $a$ does $\sum_{n=1}^{\infty}{(\frac{an}{n +1})^n}$ converge?
negative_passages.docid: 26316
negative_passages.text: Convergence of $a_n= \frac{n!}{n^n}$?
negative_passages.docid: 100574
negative_passages.text: Convergence of $\sum_n \frac{n!}{n^n}$
negative_passages.docid: 111524
negative_passages.text: Information on the sum $\sum_{n=1}^\infty \frac{\log n}{n!}$
negative_passages.docid: 102581
negative_passages.text: Does $\sum_{n=1}^{\infty} \frac{1}{n^{1 + 1/n}}$ converge?
negative_passages.docid: 43576
negative_passages.text: Convergence of $\sum _{n=1}^{\infty }\left\{ 1-n\log \frac {2n+1} {2n-1}\right\} $
negative_passages.docid: 24636
negative_passages.text: Convergence of the series $ \sum_{n=1}^{+ \infty } \frac{1}{n \cdot \ln(n) \cdot (\ln(\ln(n)))^{a}} $
negative_passages.docid: 113684
negative_passages.text: Does series with factorials converge/diverge: $\sum\limits_{n=1}^\infty \frac{4^n n!n!}{(2n)!}$?
negative_passages.docid: 74120
negative_passages.text: Find the value of $\sum_{n=1}^{\infty} \frac{2}{n}-\frac{4}{2n+1}$
negative_passages.docid: 27748
negative_passages.text: Convergence of $\sum \frac{a_n}{S_n ^{1 + \epsilon}}$ where $S_n = \sum_{i = 1} ^ n a_n$