query: Evaluating $\lim\limits_{x\to\infty}x\left(\frac{1}{e}-\left(\frac{x}{x+1}\right)^x\right)$
positive_passages.docid: 44668
positive_passages.text: Limit of $x\left(\left(1 + \frac{1}{x}\right)^x - e\right)$ when $x\to\infty$
negative_passages.docid: 109059
negative_passages.text: Evaluate $\lim\limits_{n\to \infty}\frac{1}{n+1}+\frac{1}{n+2}+\cdots+\frac{1}{6n}$
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: 36384
negative_passages.text: Q: $\lim_{n\to \infty}\left(1 + \frac{1}{n}\right)^{n} = e$
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: 49102
negative_passages.text: Evaluating $\lim_{n \to \infty}\left({^n\mathrm{C}_0}{^n\mathrm{C}_1}\dots{^n\mathrm{C}_n}\right)^{\frac{1}{n(n+1)}}$
negative_passages.docid: 138169
negative_passages.text: Finding $\lim\limits_{n \to \infty }n\int_{0}^{1}\frac{x^{n}}{1+x+x^{n}}dx$
negative_passages.docid: 63023
negative_passages.text: Evaluation of $\lim_{x\rightarrow \infty}\sqrt{x^2+x+1} -\lfloor \sqrt{x^2+x+1 }\rfloor\;,$
negative_passages.docid: 104365
negative_passages.text: Evaluate: $\lim_{n\to\infty}\left({2\sqrt n}-\sum_{k=1}^n\frac1{\sqrt k}\right)$
negative_passages.docid: 132988
negative_passages.text: $ \lim_{n \to \infty} \left(\frac 1{n^2+1}+\frac 2{n^2+2}+\frac 3{n^2+3}+\cdots +\frac n{n^2+n}\right)$
negative_passages.docid: 127107
negative_passages.text: Evaluate $\lim_{x\to \infty}\ (x!)^{1/x}$
negative_passages.docid: 135731
negative_passages.text: Is there a way to show that $e^x=\lim_{n\to \infty }\left(1+\frac{x}{n}\right)^n$?
negative_passages.docid: 43538
negative_passages.text: Show $\lim_{n \to \infty} n^{-1} E \left( \frac{1}{X}1_{[X>n^{-1}]} \right) =0$
negative_passages.docid: 63617
negative_passages.text: Evaluating limit $\lim_{k\to \infty}\prod_{r=1}^k\cos{\left(\frac {x}{2^r}\right)}$
negative_passages.docid: 101716
negative_passages.text: Find this limit: $ \lim_{n \to \infty}{(e^{\frac{1}{n}} - \frac{2}{n})^n}$
negative_passages.docid: 51622
negative_passages.text: Evaluating $\lim\limits_{x\rightarrow0}\frac{e^{-1/x^2}}{x}$
negative_passages.docid: 49012
negative_passages.text: How to evaluate $\lim_{x \to \infty}\left(\sqrt{x+\sqrt{x}}-\sqrt{x-\sqrt{x}}\right)$?