List questions from limsup-and-liminf

Published on 15 Apr 2026 - 9:08

388

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for bounded series $x_n$, prove that $\limsup(1/x_n) = 1/ \liminf( x_n)$

Published on 15 Apr 2026 - 18:09

232

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Proving that continuity and the lim sup of a given set being 0 are equivalent

Published on 13 Apr 2026 - 23:26

133

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find $\limsup$ and $\liminf$ of $a_n=\{\sqrt{n} - \lfloor\sqrt{n}\rfloor$ $n\in\mathbb{N}\}$

Published on 16 Apr 2026 - 22:53

182

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If $\lim(a_{n+1} - a_n) = 0$, prove that $P(a_n) =[\lim\inf(a_n),\lim\sup(a_n)]$

Published on 16 Apr 2026 - 18:25

118

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Equivalence of limit supremum of sequence of sets and sequence of functions

Published on 14 Apr 2026 - 9:14

271

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Evaluating $\liminf_{n\to\infty}n\{n\sqrt2\}$

Published on 10 May 2026 - 14:59

110

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Compute liminf, limsup

Published on 13 Apr 2026 - 0:42

275

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Theorem 3.37 in Baby Rudin: Any Counter-Examples In The Other Case?

Published on 15 Apr 2026 - 16:29

153

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Limes superior of $X_n>\alpha \ln(n)$

Published on 25 Mar 2026 - 17:40

227

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How can $\limsup_{x \to x_0} f(x) = f(x_0)$ for $f$ discontinuous at $x_0$?

Published on 13 Apr 2026 - 20:32

145

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Solution verification: evaluate $\lim\limits_{n \to \infty}\frac{1^{\lambda n}+2^{\lambda n}+\cdots+n^{\lambda n}}{n^{\lambda n}}$ where $\lambda>0.$

Published on 15 Apr 2026 - 9:17

231

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Does $\liminf$ distribute?

Published on 08 Apr 2026 - 16:22

142

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Show that $\limsup_{k \to \infty} 2^{-k} N_k = 0$ where $N_k$ is the number of $a_n \geq 2^{-k}$.

Published on 14 Apr 2026 - 22:28

158

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Lim Sup of n-th root of integrable functions

Published on 12 Apr 2026 - 21:40

List Question

Why is $\inf g \sup g = \frac{9}{16} $?

for bounded series $x_n$, prove that $\limsup(1/x_n) = 1/ \liminf( x_n)$

Proving that continuity and the lim sup of a given set being 0 are equivalent

find $\limsup$ and $\liminf$ of $a_n=\{\sqrt{n} - \lfloor\sqrt{n}\rfloor$ $n\in\mathbb{N}\}$

If $\lim(a_{n+1} - a_n) = 0$, prove that $P(a_n) =[\lim\inf(a_n),\lim\sup(a_n)]$

Equivalence of limit supremum of sequence of sets and sequence of functions

Evaluating $\liminf_{n\to\infty}n\{n\sqrt2\}$

Compute liminf, limsup

Theorem 3.37 in Baby Rudin: Any Counter-Examples In The Other Case?

Limes superior of $X_n>\alpha \ln(n)$

How can $\limsup_{x \to x_0} f(x) = f(x_0)$ for $f$ discontinuous at $x_0$?

Solution verification: evaluate $\lim\limits_{n \to \infty}\frac{1^{\lambda n}+2^{\lambda n}+\cdots+n^{\lambda n}}{n^{\lambda n}}$ where $\lambda>0.$

Does $\liminf$ distribute?

Show that $\limsup_{k \to \infty} 2^{-k} N_k = 0$ where $N_k$ is the number of $a_n \geq 2^{-k}$.

Lim Sup of n-th root of integrable functions

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