Question

How can we solve this limit: $\lim _{x\to \infty \:}\left(\frac{\tan\left(x\right)}{x}\right)$?

score 714 · Answer 1 · 2016-01-17 11:31:29

714

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How can we solve this limit: $\lim _{x\to \infty \:}\left(\frac{\tan\left(x\right)}{x}\right)$?

Published on 17 Jan 2016 - 11:31

score 264 · Answer 2 · 2016-01-18 02:21:25

264

Views

How to prove the limit inferior of a bounded squence exists?

Published on 18 Jan 2016 - 2:21

score 1.3k · Answer 3 · 2016-01-19 14:31:22

1.3k

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Prove that $\lim \inf \dfrac{x_{n+1}}{x_n}\leq \lim \inf x_n^{1\over n} \leq \lim \sup x_n^{1\over n} \leq \lim \sup \dfrac{x_{n+1}}{x_n}. $

Published on 19 Jan 2016 - 14:31

score 115 · Answer 4 · 2016-01-24 20:55:27

Limit superior and inferior, giving an example to show that it is possible to have ($a_n$) $>$ $L$ for infinitely many $n$

score 300 · Answer 5 · 2016-01-24 22:26:23

300

Views

Showing an inequality of LimSup: $\limsup(x_n+y_n)\geq\limsup(x_n)+\liminf(y_n)$

Published on 24 Jan 2016 - 22:26

score 1.1k · Answer 6 · 2016-01-25 02:03:42

1.1k

Views

Probability of lim sup, lim inf for sequence of random variables.

Published on 25 Jan 2016 - 2:03

score 248 · Answer 7 · 2016-01-25 13:14:52

248

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Show that $\limsup_{n \to \infty}a_nb_n= \limsup_{n \to \infty}a_n \cdot \lim_{n \to \infty}b_n$

Published on 25 Jan 2016 - 13:14

score 2.1k · Answer 8 · 2016-01-25 20:04:46

2.1k

Views

Limsup of a sequence is greater then the limsup of a subsequence?

Published on 25 Jan 2016 - 20:04

score 217 · Answer 9 · 2026-03-29 10:07:54

217

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Calculating a Hausdorff Dimension from Formula

Published on 29 Mar 2026 - 10:07

score 1.6k · Answer 10 · 2016-01-28 18:01:51

1.6k

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Proving $\lim \sup (c a_n) = c \cdot \lim \sup a_n$

Published on 28 Jan 2016 - 18:01

score 38 · Answer 11 · 2016-01-31 05:52:08

38

Views

Show that $a = \limsup_{n\to\infty} a_n$.

Published on 31 Jan 2016 - 5:52

score 193 · Answer 12 · 2016-02-13 20:17:48

193

Views

Prove that $\liminf_{n\rightarrow\infty}s_n\leqslant \liminf_{n\rightarrow\infty}\sigma_n$ for $\sigma_n=n^{-1}(s_1+...+s_n)$.

Published on 13 Feb 2016 - 20:17

score 56 · Answer 13 · 2016-02-14 17:29:37

56

Views

How lim sups here converted to appropriate limits?

Published on 14 Feb 2016 - 17:29

score 66 · Answer 14 · 2016-02-14 22:16:30

66

Views

Prove that $\sum_{k=1}^\infty a_k x^k$ converges absolutely for all $|x|<1/a$ if $a\ne0$ and for all $x\in\mathbb R$ if $a=0$.

Published on 14 Feb 2016 - 22:16

score 209 · Answer 15 · 2016-02-16 00:44:13

209

Views

How to prove that $\limsup \{a_n\}=-\liminf \{-a_n\}$

Published on 16 Feb 2016 - 0:44

List Question

How can we solve this limit: $\lim _{x\to \infty \:}\left(\frac{\tan\left(x\right)}{x}\right)$?

How to prove the limit inferior of a bounded squence exists?

Prove that $\lim \inf \dfrac{x_{n+1}}{x_n}\leq \lim \inf x_n^{1\over n} \leq \lim \sup x_n^{1\over n} \leq \lim \sup \dfrac{x_{n+1}}{x_n}. $

Limit superior and inferior, giving an example to show that it is possible to have ($a_n$) $>$ $L$ for infinitely many $n$

Showing an inequality of LimSup: $\limsup(x_n+y_n)\geq\limsup(x_n)+\liminf(y_n)$

Probability of lim sup, lim inf for sequence of random variables.

Show that $\limsup_{n \to \infty}a_nb_n= \limsup_{n \to \infty}a_n \cdot \lim_{n \to \infty}b_n$

Limsup of a sequence is greater then the limsup of a subsequence?

Calculating a Hausdorff Dimension from Formula

Proving $\lim \sup (c a_n) = c \cdot \lim \sup a_n$

Show that $a = \limsup_{n\to\infty} a_n$.

Prove that $\liminf_{n\rightarrow\infty}s_n\leqslant \liminf_{n\rightarrow\infty}\sigma_n$ for $\sigma_n=n^{-1}(s_1+...+s_n)$.

How lim sups here converted to appropriate limits?

Prove that $\sum_{k=1}^\infty a_k x^k$ converges absolutely for all $|x|<1/a$ if $a\ne0$ and for all $x\in\mathbb R$ if $a=0$.

How to prove that $\limsup \{a_n\}=-\liminf \{-a_n\}$

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