Question

Existence of lim sup/lim inf for bounded positive sequences

score 2.2k · Answer 1 · 2016-02-17 19:38:43

2.2k

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Existence of lim sup/lim inf for bounded positive sequences

Published on 17 Feb 2016 - 19:38

score 440 · Answer 2 · 2016-02-18 03:43:28

440

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Problem with finding an ordered subsequence of a bounded sequence that converges to lim inf or lim sup

Published on 18 Feb 2016 - 3:43

score 159 · Answer 3 · 2016-02-22 20:08:04

159

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Adherence values of a sequence

Published on 22 Feb 2016 - 20:08

score 435 · Answer 4 · 2016-02-27 08:53:01

435

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Properties of limsup $\limsup \sqrt{a_n} \le \sqrt{\limsup a_n}$

Published on 27 Feb 2016 - 8:53

score 137 · Answer 5 · 2016-02-27 21:16:42

137

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Prove that $\liminf_{n→∞} s_n \le \liminf_{n→∞} σ_n$

Published on 27 Feb 2016 - 21:16

score 4.1k · Answer 6 · 2016-02-28 11:04:47

4.1k

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Lim inf $ (x_n + y_n)$ less than or equal to lim inf $x_n +$ lim sup $y_n$

Published on 28 Feb 2016 - 11:04

score 489 · Answer 7 · 2016-02-28 15:44:39

489

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Show that $\liminf(\sqrt{x_n})=\sqrt{\liminf x_n}$

Published on 28 Feb 2016 - 15:44

score 170 · Answer 8 · 2016-03-02 14:15:22

170

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Positive, real, bounded sequence $(X_n)$. Prove that $\liminf \sqrt{X_n} = \sqrt{\liminf X_n}$

Published on 02 Mar 2016 - 14:15

score 972 · Answer 9 · 2016-03-04 08:47:31

972

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What does this set theory term mean: $x\in \bigcup_{k=1}^{\infty}\bigcap_{n=k}^{\infty}A_{n}.$?

Published on 04 Mar 2016 - 8:47

score 91 · Answer 10 · 2016-03-05 21:35:30

91

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Proof $\liminf_{n\rightarrow\infty}a_n=\limsup_{n\rightarrow\infty}a_n=\lim_{n\rightarrow\infty}a_n$

Published on 05 Mar 2016 - 21:35

score 100 · Answer 11 · 2016-03-06 14:54:15

100

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Prove $\,\displaystyle\limsup_{n\to\infty} s_n=m\,$ if $\,m=\sup\left\{s_n \mid h\ge 1\right\}\lt \infty\,$ and sup not attained

Published on 06 Mar 2016 - 14:54

score 225 · Answer 12 · 2016-03-07 12:14:51

225

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How to show that if either $\{a_k\}$ or $\{b_k\}$ converges, equality holds. (lim sup, lim inf)

Published on 07 Mar 2016 - 12:14

score 360 · Answer 13 · 2016-03-16 20:08:54

360

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Finding $\liminf$ and $\limsup$ of $A_n = (\sin (n) -1,\sin (n) + 1)$?

Published on 16 Mar 2016 - 20:08

score 588 · Answer 14 · 2016-03-17 14:31:34

588

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Example that $\lim \sup (x_n\cdot y_n)<\lim \sup (x_n)\cdot \lim \sup (y_n)$

Published on 17 Mar 2016 - 14:31

score 140 · Answer 15 · 2016-03-23 15:52:45

140

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if $\lim \sup a_n = l \in \mathbb R$, then given $\epsilon > 0, \exists N$ such as $a_n < l + \epsilon, \forall n \geq N$

Published on 23 Mar 2016 - 15:52

List Question

Existence of lim sup/lim inf for bounded positive sequences

Problem with finding an ordered subsequence of a bounded sequence that converges to lim inf or lim sup

Adherence values of a sequence

Properties of limsup $\limsup \sqrt{a_n} \le \sqrt{\limsup a_n}$

Prove that $\liminf_{n→∞} s_n \le \liminf_{n→∞} σ_n$

Lim inf $ (x_n + y_n)$ less than or equal to lim inf $x_n +$ lim sup $y_n$

Show that $\liminf(\sqrt{x_n})=\sqrt{\liminf x_n}$

Positive, real, bounded sequence $(X_n)$. Prove that $\liminf \sqrt{X_n} = \sqrt{\liminf X_n}$

What does this set theory term mean: $x\in \bigcup_{k=1}^{\infty}\bigcap_{n=k}^{\infty}A_{n}.$?

Proof $\liminf_{n\rightarrow\infty}a_n=\limsup_{n\rightarrow\infty}a_n=\lim_{n\rightarrow\infty}a_n$

Prove $\,\displaystyle\limsup_{n\to\infty} s_n=m\,$ if $\,m=\sup\left\{s_n \mid h\ge 1\right\}\lt \infty\,$ and sup not attained

How to show that if either $\{a_k\}$ or $\{b_k\}$ converges, equality holds. (lim sup, lim inf)

Finding $\liminf$ and $\limsup$ of $A_n = (\sin (n) -1,\sin (n) + 1)$?

Example that $\lim \sup (x_n\cdot y_n)<\lim \sup (x_n)\cdot \lim \sup (y_n)$

if $\lim \sup a_n = l \in \mathbb R$, then given $\epsilon > 0, \exists N$ such as $a_n < l + \epsilon, \forall n \geq N$

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