query: If $x>0$ is a real number, show that $\lim_{n\rightarrow{\infty}}x^{1/n}=1$.
positive_passages.docid: 158153
positive_passages.text: Prove: $ \lim_{n\rightarrow\infty} x ^ {\left(\frac 1 n\right)} = 1 $
negative_passages.docid: 30160
negative_passages.text: How to show that $\lim_{n \to +\infty} n^{\frac{1}{n}} = 1$?
negative_passages.docid: 72693
negative_passages.text: Prove: $\lim_{x\to\infty}x^{2/3}((x+1)^{1/3}-x^{1/3})=1/3$
negative_passages.docid: 44129
negative_passages.text: If $f:\mathbb{R}\rightarrow \mathbb{R}$ is differentiable and $\lim_{x\to \infty } f^\prime(x)=0$ show that $\lim _{x\to \infty } (f(x+1)-f(x))=0$.
negative_passages.docid: 137609
negative_passages.text: Proving $\lim_{n\rightarrow\infty} n(2^{1/n} - 1) = \log 2$
negative_passages.docid: 101630
negative_passages.text: Limit $\lim_{n\to\infty}\sqrt n(\sqrt[n]x-1)$
negative_passages.docid: 95575
negative_passages.text: If $f(s) = (1+s)^{(1+s)^{(1+s)/s}/s}$, show that $\lim_{s \to \infty} f(s)/s = 1$.
negative_passages.docid: 66441
negative_passages.text: Prove that $|x|<1$ implies that $\lim_{n \to \infty} x^n=0$
negative_passages.docid: 42251
negative_passages.text: Limit of non-negative real root of $x^n+x^{n-1}+x-1=0$ as $n \to \infty$
negative_passages.docid: 47668
negative_passages.text: Show that $lim_{n \rightarrow \infty}m(O_n)=m(E)$ when $E$ is compact.
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: 80440
negative_passages.text: Limit of $(x_n)$ with $0<x_1<1$ and $x_{n + 1} = x_n - x_n^{n + 1}$
negative_passages.docid: 82775
negative_passages.text: if $a>1$, Prove that $\lim a^{1\over n}=1$
negative_passages.docid: 2877
negative_passages.text: Show $\sum\limits_{n=0}^{\infty}{2n \choose n}x^n=(1-4x)^{-1/2}$
negative_passages.docid: 126749
negative_passages.text: Evaluate $\lim_{x \rightarrow 0} x^x$
negative_passages.docid: 152640
negative_passages.text: show that $\lim(\pi(x)/x) = 0$
negative_passages.docid: 41659
negative_passages.text: Limit as $x\to 0$ of $x\sin(1/x)$