Show that $\underset{n\rightarrow\infty}{\lim}{\sup}\sqrt[n]{x_n}\leq \underset{n\rightarrow\infty}\lim{\sup}\frac{x_{n+1}}{x_n}$
141496
Could someone make the proof into a hinted exercise?
45988
limit of Holder norms: $\sup\limits_{x\in [a,b]} f(x) = \lim\limits_{n\rightarrow\infty} \left(\int_a^b (f(x))^n \;dx\right)^{\frac{1}{n}}$
3111
How to prove that if $\lim_{n \rightarrow \infty}a_n=A$, then $\lim_{n \rightarrow \infty}\frac{a_1+...+a_n}{n}=A$
154506
Evaluating $\lim_{n\rightarrow\infty} (\frac{(1+\frac{1}{n})^n}{e})^n$
102523
Show that $\lim\limits_{n \to \infty} \sup\limits_{k \geq n} \left(\frac{1+a_{k+1}}{a_k}\right)^k \ge e$ for any positive sequence $\{a_n\}$
27156
Sequence Limit: $\lim\limits_{n \rightarrow \infty}{n\,x^n}$
68609
Let $a_{n+1}=\sqrt{a_1+a_2+\cdots+a_n}$ .Prove that $ \lim\limits_{n \rightarrow \infty} \frac{a_n}{n}=\frac{1}{2}$
11834
Prove that $\liminf x_n = -\limsup (-x_n)$
2882
Limit points of the set $\{\frac {\varphi(n) }n : n\in \mathbb{N}\}$
13486
Show $\lim \limits_{n \to \infty} \frac{a_{n+1}}{a_n} = \|f\|_{\infty}$ for $f \in L^{\infty}$
82204
Prove $ \lim_{n\to\infty}\sqrt[n]{p(n)}=1 $ for polynomial
57600
Show $\lim\limits_{a \rightarrow + \infty} \int_0^{\infty} \frac{1}{1+y^2}e^{-ay} dy =0 $
75268
Proving that $\lim_{n\rightarrow \infty} \frac{n^k}{2^n}=0$
33976
Prove that $\lim_{n \to \infty} \sqrt[n]{a} = 1$ using only the basic properties of sequences
66824
Two definitions of $\limsup$
88425
Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
107842
Behaviour of ($\overline{a}_n)_{n=1}^{\infty}$ and ($\underline{a}_n)_{n=1}^{\infty}$