show that $\lim\sqrt[n]{x_1x_2\dots x_n}=\alpha$
107142
If $(x_n) \to x$ then $(\sqrt[n]{x_1x_2\cdots x_n}) \to x$
60036
How to prove this limit exists: $a_{n+2}=\sqrt{a_{n+1}}+\sqrt{a_{n}}$
75639
Showing that $\sqrt[3]{2}\notin\Bbb Q(\alpha_1,...,\alpha_k)$ where $\alpha_i^2\in\Bbb Q\ \forall i$
5728
How to prove $\lim_{n \to \infty} \sqrt{n}(\sqrt[n]{n} - 1) = 0$?
67645
Prove that $\displaystyle{\lim_{n \to \infty}a_n ^{1/k}}= a^{1/k}$ if $a_n \ge 0$ for all $n$ and $\displaystyle{\lim_{n \to \infty}a_n}= a$
119106
Compute: $\lim_{x\to 0}\frac{\sqrt[m]{\cos(\alpha x)}-\sqrt[n]{\cos{(\beta x)}}}{x^2},\;m,n\in\mathbb N,\alpha,\beta\in\mathbb R$
64932
Show that $\lim_{x\to a^{+}} g(x) =g(a)$
57095
How do I prove the sequence $x_{n+1}=\sqrt{\alpha +x_n}$, with $x_0=\sqrt \alpha$ converges? ( boundedness?)
142509
If $\alpha\in (0,1]$ and $x_n=\alpha x_{n-1}+(1-\alpha)x_{n-2}$, show that the sequence $\{x_n\}$ is convergent.
120010
Show that $\aleph_{\alpha}^{\aleph_{1}} = \aleph_{\alpha}^{\aleph_{0}}\cdot 2^{\aleph_1}$
80440
Limit of $(x_n)$ with $0<x_1<1$ and $x_{n + 1} = x_n - x_n^{n + 1}$
53213
How to prove that $\lim(\underset{k\rightarrow\infty}{\lim}(\cos(|n!\pi x|)^{2k}))=\chi_\mathbb{Q}$
108971
Finding the limit of $\sqrt[n]{{kn \choose n}}$
157847
If $x_n \to 0$, show that $\sqrt{x_n} \to 0$
101630
Limit $\lim_{n\to\infty}\sqrt n(\sqrt[n]x-1)$
156478
Prove that $\lim_{n\rightarrow\infty}\frac{x_1^2+x_2^2+\cdots+x_n^2}{n^2}=0$
41434
Show that: $\lim \limits_{n \rightarrow+\infty} \int_{0}^{1}{f(x^n)dx}=f(0)$