List questions from limsup-and-liminf

Published on 09 Oct 2020 - 14:04

94

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Show that $\lim \sup |a_n + b_n|^{1/n} \leq \frac1r \text{ and } \lim\sup |c\;a_n|^{1/n} \leq \frac1r$

Published on 11 Oct 2020 - 21:55

53

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Bounds on limsup and liminf

Published on 12 Oct 2020 - 2:44

462

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Intuition of $\limsup_n (X_n - \log n)/\log \log n$, for exponential random variable

Published on 16 Oct 2020 - 5:05

79

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Two inequalities along the proof of nondifferentiability of Brownian motion: why do they hold true?

Published on 22 Oct 2020 - 20:28

235

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Step on a proof that the root test is stronger than the ratio test.

Published on 24 Oct 2020 - 0:22

66

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$\limsup_n \left[\frac{q_n}{2^{p_n}};\frac{q_n+1}{2^{p_n}}\right[=[0;1[?$

Published on 24 Oct 2020 - 22:32

88

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Question about a step in the proof of $\lim_{p \to \infty} \|x\|_p = \|x\|_{\infty}$

Published on 25 Oct 2020 - 14:12

206

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Calculate limit inferior and limit superior of $v_{n}$.

Published on 25 Oct 2020 - 16:51

45

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how can I find the limit superior and limit inferior of this set?

Published on 25 Oct 2020 - 22:48

90

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If $0\leq X_k < 1$, then $\lim_{k\to\infty} \prod_{i}^{k}X_i =0$ almost surely?

Published on 26 Oct 2020 - 15:52

43

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$\mathbb{E}[M_{a}]\geq \mathbb{E}[M_{b}]$ with $a,b$ limited stopping times and $M$ sub-martingale

Published on 02 Apr 2026 - 17:42

190

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$\limsup (a_n +b_n) = a + \limsup b_n$ when $a_n$ converges to $a$

Published on 31 Oct 2020 - 2:26

58

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$\limsup_{n\to \infty} \sqrt[n]{\lvert \lvert ((a_n)^1, (a_n)^2, (a_n)^3 \rvert \rvert}\leq 1$?

Published on 31 Oct 2020 - 10:27

41

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Proving that $ \liminf_{n\to \infty} x_n=\min \mathcal{L}((x_n)_{n\ge 1})$

Published on 02 Nov 2020 - 15:31

List Question

Limsup of $\sin(rz)$ as $r\to \infty$

Show that $\lim \sup |a_n + b_n|^{1/n} \leq \frac1r \text{ and } \lim\sup |c\;a_n|^{1/n} \leq \frac1r$

Bounds on limsup and liminf

Intuition of $\limsup_n (X_n - \log n)/\log \log n$, for exponential random variable

Two inequalities along the proof of nondifferentiability of Brownian motion: why do they hold true?

Step on a proof that the root test is stronger than the ratio test.

$\limsup_n \left[\frac{q_n}{2^{p_n}};\frac{q_n+1}{2^{p_n}}\right[=[0;1[?$

Question about a step in the proof of $\lim_{p \to \infty} \|x\|_p = \|x\|_{\infty}$

Calculate limit inferior and limit superior of $v_{n}$.

how can I find the limit superior and limit inferior of this set?

If $0\leq X_k < 1$, then $\lim_{k\to\infty} \prod_{i}^{k}X_i =0$ almost surely?

$\mathbb{E}[M_{a}]\geq \mathbb{E}[M_{b}]$ with $a,b$ limited stopping times and $M$ sub-martingale

$\limsup (a_n +b_n) = a + \limsup b_n$ when $a_n$ converges to $a$

$\limsup_{n\to \infty} \sqrt[n]{\lvert \lvert ((a_n)^1, (a_n)^2, (a_n)^3 \rvert \rvert}\leq 1$?

Proving that $ \liminf_{n\to \infty} x_n=\min \mathcal{L}((x_n)_{n\ge 1})$

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