query: How is $\displaystyle\lim_{n\to\infty}{(1+1/n)^n} = e$?
positive_passages.docid: 154286
positive_passages.text: Evaluating $\lim_{n \to \infty} (1 + 1/n)^{n}$
negative_passages.docid: 140574
negative_passages.text: Find $\lim_{n\to \infty} \int_0^1 nx^n e^{x^2} dx$
negative_passages.docid: 8387
negative_passages.text: Evaluate $\lim_{n \rightarrow \infty} \frac {[(n+1)(n+2)\cdots(n+n)]^{1/n}}{n}$
negative_passages.docid: 35260
negative_passages.text: Evaluate the limit $\displaystyle\lim_{x \to 0}\frac{(e-\left(1 + x\right)^{1/x})}{\tan x}$.
negative_passages.docid: 103870
negative_passages.text: $3.\lim_{n\to\infty}\langle x,e_n\rangle=?$
negative_passages.docid: 17872
negative_passages.text: Evaluate $\lim\limits_{n\to\infty}\frac{\sum_{k=1}^n k^m}{n^{m+1}}$
negative_passages.docid: 115028
negative_passages.text: If $e=\lim\limits_{x\to \infty} (1+x^{-1})^x$, why doesn't $e=1$?
negative_passages.docid: 13486
negative_passages.text: Show $\lim \limits_{n \to \infty} \frac{a_{n+1}}{a_n} = \|f\|_{\infty}$ for $f \in L^{\infty}$
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: 43852
negative_passages.text: Evaluate $\lim_{x\to 0}\frac{e^{(x+1)^{1/x}}-(x+1)^{e/x}}{x^2}$
negative_passages.docid: 54367
negative_passages.text: How to calculate $\lim_{n\to\infty}(1+1/n^2)(1+2/n^2)\cdots(1+n/n^2)$?
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: 73670
negative_passages.text: Help with Limit: $\lim_{n \to \infty} \frac{(2 n)! e^n (n)^n}{n! (2 n)^{2 n}}$
negative_passages.docid: 142249
negative_passages.text: Show that $\lim_{n\to \infty} \int_E \cos^2(nx + a_n) dx = \frac{1}{2}m(E)$
negative_passages.docid: 22575
negative_passages.text: Prove that $\lim\limits_{n\rightarrow\infty} \left(1+\frac{1}{a_{n}} \right)^{a_{n}}=e$ if $\lim\limits_{n\rightarrow\infty} a_{n}=\infty$
negative_passages.docid: 117370
negative_passages.text: $\lim_{n\to\infty} \left(1+\frac{2}{n}\right)^{n^2} e^{-2n}$
negative_passages.docid: 73812
negative_passages.text: Does $\lim \limits_ {n\to \infty}\ \frac{n}{n+1}$ equal $1$?