query: Compute $\lim_{n\rightarrow\infty}\left(\frac{n+1}{n}\right)^{n^2}\cdot\frac{1}{e^n}.$
positive_passages.docid: 18353
positive_passages.text: Evaluate of $\lim_{n\rightarrow \infty}\left(\frac{n+1}{n}\right)^{n^2}\cdot \frac{1}{e^n}$
negative_passages.docid: 12378
negative_passages.text: Find the limit $\displaystyle\lim_{n\rightarrow\infty}{(1+1/n)^{n^2}e^{-n}}$?
negative_passages.docid: 144403
negative_passages.text: Limit $\lim_{x\rightarrow +\infty}\sqrt{x}e^{-x}\left(\sum_{k=1}^{\infty}\frac{x^{k}}{k!\sqrt{k}}\right)$
negative_passages.docid: 84384
negative_passages.text: Evaluate $\lim_{n\to \infty}\left(\frac{1}{\sqrt{n(n+1)}}+\frac{1}{\sqrt{(n+1)(n+2)}}+\cdots+\frac{1}{\sqrt{(2n-1)2n}}\right)$
negative_passages.docid: 111418
negative_passages.text: Finding lim${_{n \rightarrow \infty}}\left( \frac{n^3}{2^n} \right)$
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: 75567
negative_passages.text: Find $\lim_{n \to \infty} \left[\frac{(n+1)^{n + 1}}{n^n} - \frac{n^{n}}{(n-1)^{n-1}} \right]$ (a question asked at trivia)
negative_passages.docid: 115819
negative_passages.text: Evaluate $\lim \limits_{n\rightarrow\infty}\sin^2(\pi\sqrt{n^2 + n})$
negative_passages.docid: 120336
negative_passages.text: Evaluation of $\lim_{n\rightarrow \infty}\binom{2n}{n}^{\frac{1}{n}}$
negative_passages.docid: 76756
negative_passages.text: A convergence proof: $\lim_{n\to\infty} \left(1+n^2\right)^{\frac1n}$
negative_passages.docid: 50334
negative_passages.text: What is $\lim_{n \rightarrow \infty}\sum\limits_{k = 1}^n\frac{k}{n^2}$?
negative_passages.docid: 79256
negative_passages.text: How should I calculate $\lim_{n\rightarrow \infty} \frac{1^n+2^n+3^n+...+n^n}{n^n}$
negative_passages.docid: 72568
negative_passages.text: Calculation of $\lim_{n\to \infty}\prod_{r=1}^{n} \left(1+\frac{r}{n}\right)^{\frac{1}{n}}$
negative_passages.docid: 129113
negative_passages.text: Calculate $\lim_{n\rightarrow +\infty}\binom{2n} n$
negative_passages.docid: 50398
negative_passages.text: Limit $\lim\limits_{n\to\infty}\left(\frac{n}{n^2+1}+\frac{n}{n^2+2}+\frac{n}{n^2+3}+\cdots+\frac{n}{n^2+n}\right)$
negative_passages.docid: 26211
negative_passages.text: Computing $\lim_{x \to \infty} x \biggl[ \frac{1}{e} - \left( \frac{x}{x+1} \right)^x \biggr]$
negative_passages.docid: 43703
negative_passages.text: Find $\lim _{x\to \infty }\left(x\left(\ln\left(x+1\right)-\ln x\right)\right) $