How to show $\lim_{n \to \infty} \sqrt[n]{a^n+b^n}=\max \{a,b\}$?
30167
Convergence of $\sqrt[n]{x^n+y^n}$ (for $x, y > 0$)
128181
Find $\lim_{n\to\infty}{\sqrt{n+1}-\sqrt{n}}$ with basic methods
83318
How to compute the limit $\lim_{n \to \infty} \sqrt[n]{a_1^n + \cdots + a_m^n}$?
133244
Finding $\lim_{n \to \infty} n(\sqrt[n]{2} - 1)$
60036
How to prove this limit exists: $a_{n+2}=\sqrt{a_{n+1}}+\sqrt{a_{n}}$
67645
Prove that $\displaystyle{\lim_{n \to \infty}a_n ^{1/k}}= a^{1/k}$ if $a_n \ge 0$ for all $n$ and $\displaystyle{\lim_{n \to \infty}a_n}= a$
68891
Are the limits $\lim\limits_{n\to \infty }\left|\frac{a_{n+1}}{a_n}\right|\,$ and $\lim\limits_{n\to \infty }\sqrt[n]{|a_n|}\,$ equal?
33610
Evaluate $\displaystyle \lim_{n\to \infty}\sqrt[n]{n!}$
146663
Limit $\lim_{n \to \infty} \frac {a_n}{2^{n-1}}=\frac 4{\pi}$ for $a_{n+1}=a_n+\sqrt{1+a_n^2}$ and $a_0=0$
854
$\lim_{n\to\infty}a_nb_n=? $ given that $\lim_{n\to\infty}a_n=0$ and $\lim_{n\to\infty}b_n=\infty$
25206
How to prove that $\lim\limits_{n\to \infty}a_{n+1}=\lim\limits_{n\to \infty}a_{n}$
33976
Prove that $\lim_{n \to \infty} \sqrt[n]{a} = 1$ using only the basic properties of sequences
37277
$\lim\limits_{n \to{+}\infty}{\sqrt[n]{n!}}$ is infinite
34491
Is there a way to show that $\sqrt{p_{n}} < n$?
18079
Evaluating $\lim\limits_{x\to \infty}\sqrt[6]{x^{6}+x^{5}}-\sqrt[6]{x^{6}-x^{5}}$
15982
Limit of $b_n$ when $b_n=\frac{a_n}{n}$ and $\lim\limits_{n\to\infty}(a_{n+1}-a_n)=l$
125860
Showing that $\lim\limits_{n\to\infty}x_n$ exists, where $x_{n} = \sqrt{1 + \sqrt{2 + \sqrt{3 + ...+\sqrt{n}}}}$