query: Evaluating $\lim_{n \to \infty} n\left(1-\frac{1}{e}\left(1+\frac{1}{n}\right)^{n} \right)$
positive_passages.docid: 17329
positive_passages.text: How do I find this limit: $\lim_{n\to\infty} \left[ n-{n\over e}\left(1+{1\over n}\right)^n \right]$?
negative_passages.docid: 81997
negative_passages.text: Evaluating $\lim_{n\to \infty}\frac1{2n}\log\left({2n \choose n}\right)$
negative_passages.docid: 156546
negative_passages.text: Evaluate the limit $\lim_{n\rightarrow \infty}\frac{1}{\sqrt{n}}\left(1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\ldots+\frac{1}{\sqrt{n}}\right)$
negative_passages.docid: 74919
negative_passages.text: Finding limit of function $\lim_{x\to 0}\left(\frac{(1+x)^\frac1x}{e}\right)^\frac1x$
negative_passages.docid: 113289
negative_passages.text: finding the limit $\lim\limits_{x \to \infty }(\frac{1}{e}(1+\frac{1}{x})^x)^x$
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: 78033
negative_passages.text: Evaluating $\prod_{n=1}^{\infty}\left(1+\frac{1}{2^n}\right)$
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: 5072
negative_passages.text: To evaluate limit of sequence $\left(\left( 1 + \frac1n \right) \left( 1 + \frac2n \right)\cdots\left( 1 + \frac nn \right) \right)^{1/n}$
negative_passages.docid: 151100
negative_passages.text: Determining $\lim_{n\to\infty}\left(n^{\tfrac{1}{n}}-1\right)^n$ with only elementary math
negative_passages.docid: 1869
negative_passages.text: Why does $\lim_{n\to\infty}(1+\frac{1}{n})^n = e$ instead of $1$?
negative_passages.docid: 20843
negative_passages.text: Evaluate the limit of $\lim_{n\to\infty}\frac{1}{n^2}\left(\frac{2}{1}+\frac{9}{2}+\frac{64}{9}+\cdots+\frac{(n+1)^{n}}{n^{n-1}}\right)$
negative_passages.docid: 53109
negative_passages.text: Why is this limit $\lim_{n \to \infty}(1 + \frac{1}{n})^n$ equal to $e$?
negative_passages.docid: 56902
negative_passages.text: Evaluate $\lim_{n \to \infty} \frac{1}{n}[(n +1)(n+2) \cdots (n+n)]^{\frac{1}{n}}$
negative_passages.docid: 49128
negative_passages.text: How to prove $\lim\limits_{n \to \infty} (1+\frac1n)^n = e$?
negative_passages.docid: 35169
negative_passages.text: Finding the limit of $\left(\frac{n}{n+1}\right)^n$
negative_passages.docid: 93095
negative_passages.text: Find $\lim\limits_{n \to \infty}\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\cdots\left(1-\frac{1}{n^2}\right)$