query: the limit of (n/(n+1))^n as n->infinity
positive_passages.docid: 7309
positive_passages.text: Why $\lim\limits_{n\to \infty}\left(1+\frac{1}{n}\right)^n$ doesn't evaluate to 1?
negative_passages.docid: 26837
negative_passages.text: Limit of the sequence $\{n^n/n!\}$, is this sequence bounded, convergent and eventually monotonic?
negative_passages.docid: 78116
negative_passages.text: What is the most elementary proof that $\lim_{n \to \infty} (1+1/n)^n$ exists?
negative_passages.docid: 31866
negative_passages.text: Calculating the limit $\lim((n!)^{1/n})$
negative_passages.docid: 73934
negative_passages.text: Subadditive sequences and the limit $\sup_{n\to\infty} a_n / n$
negative_passages.docid: 41742
negative_passages.text: inverse limit of $k[x]/(x^n)$
negative_passages.docid: 12378
negative_passages.text: Find the limit $\displaystyle\lim_{n\rightarrow\infty}{(1+1/n)^{n^2}e^{-n}}$?
negative_passages.docid: 87116
negative_passages.text: Prove $ \lim_{n\to \infty}\frac{n}{n+1} = 1$ using Cauchy (epsilon) definition of a limit of a sequence
negative_passages.docid: 148492
negative_passages.text: Finding the limit of the sequence $(1 - 1/\sqrt 2) \dotsm ( 1 - 1/\sqrt {n+1})$
negative_passages.docid: 47895
negative_passages.text: Prove $\lim\limits_{n\to\infty}n^{-1/(p+1)}(1^{1^p}\cdot 2^{2^p}\cdots n^{n^p})^{n^{-p-1}}=e^{-1/(p+1)^2}$
negative_passages.docid: 37277
negative_passages.text: $\lim\limits_{n \to{+}\infty}{\sqrt[n]{n!}}$ is infinite
negative_passages.docid: 9781
negative_passages.text: How to prove that $\lim_{n \to \infty} n x^{n} = 0 $ when $0<x<1$?
negative_passages.docid: 31836
negative_passages.text: Proof of $\lim_{n\to \infty} \sqrt[n]{n}=1$
negative_passages.docid: 117039
negative_passages.text: How to show $(1/n!)^{1/n}$ goes to $0$ as $n$ goes to infinity?
negative_passages.docid: 125538
negative_passages.text: limit of $n^{\frac{1}{\sqrt{n}}}$
negative_passages.docid: 67420
negative_passages.text: Limit of quotient sequence
negative_passages.docid: 5797
negative_passages.text: Limit of the sequence $a_n=\sqrt[n+1]{(n+1)!}-\sqrt[n]{n!}$