List questions from limsup-and-liminf

Published on 17 Mar 2026 - 4:01

50

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Find the sup and inf of a set with parameter

Published on 22 Mar 2026 - 15:56

39

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Is this $\epsilon$-conditon for $\limsup$ false?

Published on 06 Feb 2018 - 6:39

50

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Upper and lower limits of 'alternating' sequence

Published on 22 Mar 2026 - 12:05

160

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Proving the upper bound of the sequence in converging power series

Published on 11 Feb 2018 - 11:57

41

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Question on whether I can apply Fatou's Lemma

Published on 18 Feb 2018 - 13:03

40

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Elementary question on inequality using $\;\liminf\;$

Published on 22 Mar 2026 - 11:14

502

Views

Let $a = \liminf x_n$, $b = \limsup x_n$. If $\lim (x_{n+1} - x_n) = 0$ then every element of $(a,b)$ is a subsequential limit of $(x_n)$

Published on 25 Feb 2018 - 23:01

1.5k

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Show that $s\in\limsup\limits_{n\to\infty} A_n$ iff there are infinitely many $n\in\mathbb{N}$ such that $s\in A_n$.

Published on 28 Feb 2018 - 15:38

199

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Density limits and sets with positive lower density

Published on 22 Mar 2026 - 7:36

315

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Find the radius of convergence of the series $\sum a_n z^n$ when: $a_n = \frac{(n!)^3}{(3n)!}$.

Published on 06 Mar 2018 - 22:21

56

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An example to show that we can have $\limsup \frac{a_{n+1}}{a_n}=1$ and Cauchy root test $\limsup a_n^{\frac{1}{n}} <1$

Published on 07 Mar 2018 - 9:55

1.2k

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Compute $\limsup |\sin^n (n)|$

Published on 22 Mar 2026 - 5:36

58

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Is $\limsup A_n=\inf_N\sup_{n\ge N} A_n$ for set?

Published on 12 Mar 2018 - 0:15

283

Views

Conditional Probability and Borel-Cantelli theorems

Published on 13 Mar 2018 - 3:47

List Question

Finding whether $\lim\sup x_n >0$

Find the sup and inf of a set with parameter

Is this $\epsilon$-conditon for $\limsup$ false?

Upper and lower limits of 'alternating' sequence

Proving the upper bound of the sequence in converging power series

Question on whether I can apply Fatou's Lemma

Elementary question on inequality using $\;\liminf\;$

Let $a = \liminf x_n$, $b = \limsup x_n$. If $\lim (x_{n+1} - x_n) = 0$ then every element of $(a,b)$ is a subsequential limit of $(x_n)$

Show that $s\in\limsup\limits_{n\to\infty} A_n$ iff there are infinitely many $n\in\mathbb{N}$ such that $s\in A_n$.

Density limits and sets with positive lower density

Find the radius of convergence of the series $\sum a_n z^n$ when: $a_n = \frac{(n!)^3}{(3n)!}$.

An example to show that we can have $\limsup \frac{a_{n+1}}{a_n}=1$ and Cauchy root test $\limsup a_n^{\frac{1}{n}} <1$

Compute $\limsup |\sin^n (n)|$

Is $\limsup A_n=\inf_N\sup_{n\ge N} A_n$ for set?

Conditional Probability and Borel-Cantelli theorems

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