Is it true that $\limsup \phi\le\limsup a_n$, where $\phi=\frac{a_1+...+a_n}n$?
46775
If $\sigma_n=\frac{s_1+s_2+\cdots+s_n}{n}$ then $\operatorname{{lim sup}}\sigma_n \leq \operatorname{lim sup} s_n$
126791
If $2a_{n+2} \le a_{n+1}+a_n$, then $\lim \sup a_n \le \frac23 a_2 + \frac13 a_1$
145772
Proving $\liminf_{n\to\infty}(-a_n)=-\limsup_{n\to\infty}(a_n)$
73934
Subadditive sequences and the limit $\sup_{n\to\infty} a_n / n$
61858
Is there $\phi(n)=n/6$
73812
Does $\lim \limits_ {n\to \infty}\ \frac{n}{n+1}$ equal $1$?
22575
Prove that $\lim\limits_{n\rightarrow\infty} \left(1+\frac{1}{a_{n}} \right)^{a_{n}}=e$ if $\lim\limits_{n\rightarrow\infty} a_{n}=\infty$
53263
Show $\sum\limits_{d|n}\phi(d) = n$.
148782
How to prove these two limits $\lim_{n\to\infty}\frac{a_{n}}{n}$ and $\lim_{n\to\infty}\frac{a_{n+1}-a_{n}}{n}$ exist?
64932
Show that $\lim_{x\to a^{+}} g(x) =g(a)$
7507
Proof that $\lim{a_n}=L$ when $n$ goes to infinity, then $\{a_n\}$ its a Cauchy Sequence
102478
$X_n\leq Y_n$ implies $\liminf X_n \leq \liminf Y_n$ and $\limsup X_n \leq \limsup Y_n$
116811
Proofs with limit superior and limit inferior: $\liminf a_n \leq \limsup a_n$
51995
Probability of $\limsup$ of a sequence of sets (Borel-Cantelli lemma)
43168
Prove that $\limsup\left(b_{n}a_{n}\right)=\limsup\left(a_{n}\right) $ when $\lim_{n\rightarrow\infty}\left(b_{n}\right)=1$
68913
Proving that $1_{\limsup A_n}=\limsup1_{A_n}$.
13486
Show $\lim \limits_{n \to \infty} \frac{a_{n+1}}{a_n} = \|f\|_{\infty}$ for $f \in L^{\infty}$