query: Compute: $\lim_\limits{n\to\infty} \sum_\limits{k=1}^n\frac{1}{1+3^k}$
positive_passages.docid: 19899
positive_passages.text: infinite series of the form $\sum\limits_{k=1}^{\infty}\frac{1}{a^{k}+1}$
negative_passages.docid: 54775
negative_passages.text: Find $\lim_{n \to \infty} n[(1+\frac{1}{n})^n - e]$
negative_passages.docid: 103833
negative_passages.text: limit $\lim_{n\to \infty }\sum_{k=1}^{n}\frac{k}{k^2+n^2}$
negative_passages.docid: 32866
negative_passages.text: How find this sum $\sum\limits_{n=0}^{\infty}\frac{1}{(3n+1)(3n+2)(3n+3)}$
negative_passages.docid: 47575
negative_passages.text: Compute the limit of $\sqrt{1-a}\sum\limits_{n=0}^{+\infty} a^{n^2}$ when $a\to1^-$
negative_passages.docid: 1098
negative_passages.text: Does $\sum\limits_{n=1}^\infty\frac{1}{\sqrt{n}+\sqrt{n+1}}$ converge?
negative_passages.docid: 105971
negative_passages.text: Convergence of $\sum \limits_{n=1}^{\infty}\sqrt{n^3+1}-\sqrt{n^3-1}$
negative_passages.docid: 5054
negative_passages.text: Calculate $\sum\limits_{k=0}^{\infty}\frac{1}{{2k \choose k}}$
negative_passages.docid: 41366
negative_passages.text: Compute $\lim\limits_{n\to\infty} \left(1+\frac{1}{n}\right)\left(1+\frac{2}{n}\right)^{{1}/{2}}\cdots\left(1+\frac{n}{n}\right)^{{1}/{n}}$
negative_passages.docid: 17713
negative_passages.text: What's the value of $\sum\limits_{k=1}^{\infty}\frac{k^2}{k!}$?
negative_passages.docid: 78167
negative_passages.text: Show that the series $\sum\limits_{n=2}^{\infty} \frac {(n^3+1)^{1/3}-n}{\log n}$ converges
negative_passages.docid: 77605
negative_passages.text: Limit of $\prod\limits_{k=2}^n\frac{k^3-1}{k^3+1}$
negative_passages.docid: 56265
negative_passages.text: limit $\lim\limits_{n\to\infty}\left(\sum\limits_{i=1}^{n}\frac{1}{\sqrt{i}} - 2\sqrt{n}\right)$
negative_passages.docid: 79646
negative_passages.text: Compute $\lim_{n\to\infty}\frac{\tfrac{n}{1}+\tfrac{n-1}{2}+\dots+\tfrac{2}{n-1}+\tfrac{1}{n}}{\ln(n!)}$
negative_passages.docid: 116019
negative_passages.text: Find the limit $\lim\limits_{n\to \infty}\sum\limits_{k=1}^{n}\left(\frac{k}{n^2}\right)^{\frac{k}{n^2}+1}$
negative_passages.docid: 40227
negative_passages.text: Compute $\lim\limits_{n\to\infty}n^2\left(\left(1+\frac1{n+1}\right)^{n+1}-\left(1+\frac1n\right)^n\right)$
negative_passages.docid: 37148
negative_passages.text: How to evaluate $ \lim \limits_{n\to \infty} \sum \limits_ {k=1}^n \frac{k^n}{n^n}$?