query: Why $\lim_{n\to \infty} \left(1+ \frac 1n \right)^n=e$ doesn't imply $\lim_{n\to \infty} \left(1+\frac 1n \right)≠1?$
positive_passages.docid: 26338
positive_passages.text: Does $1^{\infty}=e$ or $1^{\infty}=1$?
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: 96297
negative_passages.text: Limit involving binomial coefficients: $\lim_{n\to\infty}\left(\binom{n}{0}\binom{n}{1}\dots\binom{n}{n}\right)^{\frac{1}{n(n+1)}}$
negative_passages.docid: 153269
negative_passages.text: Find $\lim_{n \to \infty} \left( \frac{3^{3n}(n!)^3}{(3n)!}\right)^{1/n}$
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: 101687
negative_passages.text: $ \lim_{x\to o} \frac{(1+x)^{\frac1x}-e+\frac{ex}{2}}{ex^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: 79299
negative_passages.text: Strange behavior of $\lim_{x\to0}\frac{\sin\left(x\sin\left(\frac1x\right)\right)}{x\sin\left(\frac1x\right)}$
negative_passages.docid: 119200
negative_passages.text: When does $\lim_{n\to\infty}f(x+\frac{1}{n})=f(x)$ a.e. fail
negative_passages.docid: 64169
negative_passages.text: Why isn't $\lim \limits_{x\to\infty}\left(1+\frac{1}{x}\right)^{x}$ equal to $1$?
negative_passages.docid: 94910
negative_passages.text: How does one show that $\lim_{x\rightarrow\infty}\left(1+\frac{1}{x}\right)^x$ converges?
negative_passages.docid: 11912
negative_passages.text: Is it true that $\displaystyle \left( \lim_{n \to \infty} x_n \right)^\alpha = \lim_{n \to \infty} x_n^\alpha $
negative_passages.docid: 51869
negative_passages.text: Why does $\;\lim_{n\to \infty }\frac{n}{n!^{1/n}}=e$?
negative_passages.docid: 30160
negative_passages.text: How to show that $\lim_{n \to +\infty} n^{\frac{1}{n}} = 1$?
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: 73865
negative_passages.text: Find $\lim_{n\to\infty}n\left(\sum_{i=1}^{n}\dfrac{1}{(n+i)^2}\right)$
negative_passages.docid: 148170
negative_passages.text: Difficulty in evaluating a limit: $\lim_{x \to \infty} \frac{e^x}{\left(1+\frac{1}{x}\right)^{x^2}}$