lim sup $(x_n)$ = largest limit point of $(x_n)$
69103
$\limsup$ and cluster points
73906
Prove that subsequence converges to limsup
138052
How to work out the limit of  this bounded sequence?
99975
Find the Limit (n to infinity)
41434
Show that: $\lim \limits_{n \rightarrow+\infty} \int_{0}^{1}{f(x^n)dx}=f(0)$
15982
Limit of $b_n$ when $b_n=\frac{a_n}{n}$ and $\lim\limits_{n\to\infty}(a_{n+1}-a_n)=l$
88064
Prove: $a_n \leq b_n \implies \limsup a_n \leq \limsup b_n$
116811
Proofs with limit superior and limit inferior: $\liminf a_n \leq \limsup a_n$
91310
Does a limit point always exist?
65137
Evaluating $\lim\limits_{n\to\infty}(a_1^n+\dots+a_k^n)^{1\over n}$ where $a_1 \ge \cdots\ge a_k \ge 0$
31889
The limit as $n$ approaches infinity of $n(a^{1/n}-1)$
67420
Limit of quotient sequence
50019
Prove $0$ is a partial limit of $a_n$
16718
Doubt about step of the proof that $\limsup\limits_{n\to\infty}\left|\sum\limits_{\ell=1}^mz^n_\ell\right|^{1/n}=\max\limits_{1\le\ell\le m}|z_\ell|$
125011
Show lim sup (an) = lim inf (an) for increasing for increasing sequence of subsets.
117640
Prove that $\lim \inf \dfrac{x_{n+1}}{x_n}\leq \lim \inf x_n^{1\over n} \leq \lim \sup x_n^{1\over n} \leq \lim \sup \dfrac{x_{n+1}}{x_n}. $
437
Show that $\lim_{n\to\infty} \sqrt[n]{a^{n} + b^{n}} = \max(a, b)$