query: Why is$ (1+\frac{1}{n})^n=e$ when n goes to infinity?
positive_passages.docid: 17809
positive_passages.text: How come such different methods result in the same number, $e$?
negative_passages.docid: 7309
negative_passages.text: Why $\lim\limits_{n\to \infty}\left(1+\frac{1}{n}\right)^n$ doesn't evaluate to 1?
negative_passages.docid: 17754
negative_passages.text: Intuitive Understanding of the constant "$e$"
negative_passages.docid: 77517
negative_passages.text: Why is this sum a representation of e?
negative_passages.docid: 29213
negative_passages.text: Limit of 1/x as x approaches infinity
negative_passages.docid: 11489
negative_passages.text: Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$
negative_passages.docid: 13796
negative_passages.text: What is the value of $\prod_{n=1}^\infty (1+\frac{1}{n^2})$?
negative_passages.docid: 25652
negative_passages.text: Intuitive explanation for $\mathbb{E}X= \int_0^\infty 1-F(x) \, dx$
negative_passages.docid: 86653
negative_passages.text: Elementary question about the limit $\big( 1 - \frac 1 {\sqrt n}\big )^n$, $n\to\infty$.
negative_passages.docid: 14031
negative_passages.text: Why does the series $\sum_{n=1}^\infty\frac1n$ not converge?
negative_passages.docid: 108917
negative_passages.text: Use $\delta-\epsilon$ to show that $\lim_{n\to\infty} a^{\frac{1}{n}} = 1$?
negative_passages.docid: 61963
negative_passages.text: Proving that $\sum\limits_{n=0}^{\infty }\frac{1}{(2n)!!}=\sqrt{e}$
negative_passages.docid: 26226
negative_passages.text: Proving $\lim \limits_{n\to +\infty } \left(1+\frac{x}{n}\right)^n=\text{e}^x$.
negative_passages.docid: 15292
negative_passages.text: Elementary proof for $\lim\limits_{n \to\infty}\frac{n!e^n}{n^n} = +\infty$
negative_passages.docid: 141540
negative_passages.text: What is wrong with the following "proof" that $e=1$?
negative_passages.docid: 59427
negative_passages.text: convergence to infinity of$ (2^n + 3^n)^{\frac{1}{n}}$ (as $n \to \infty$)
negative_passages.docid: 40837
negative_passages.text: Why $e^{i(π/3)} \ne -1$?