Question

Consequences of $\limsup\limits_{n \rightarrow \infty}(a_n)=1$.

score 56 · Answer 1 · 2015-12-05 21:59:32

56

Views

Consequences of $\limsup\limits_{n \rightarrow \infty}(a_n)=1$.

Published on 05 Dec 2015 - 21:59

score 1.2k · Answer 2 · 2015-12-06 13:59:33

1.2k

Views

Can we always find the infimum and supremum of a sequence?

Published on 06 Dec 2015 - 13:59

score 56 · Answer 3 · 2015-12-06 16:20:27

56

Views

If $\limsup_{n\to\infty} \ x_{n} =-\infty$ then why $\lim_{n\to\infty} \ x_{n} =-\infty$?

Published on 06 Dec 2015 - 16:20

score 226 · Answer 4 · 2015-12-06 19:46:45

If $\lim_{x \to \infty} x_n = \liminf_{n \to \infty} x_n = \limsup_{n \to \infty} x_n= -\infty$ does it exist a convergent subsequence of $x_n$?

score 109 · Answer 5 · 2015-12-07 20:12:59

109

Views

reference on limsup and liminf for functions

Published on 07 Dec 2015 - 20:12

score 74 · Answer 6 · 2015-12-08 18:05:14

74

Views

If $\limsup_{n\to\infty} \ x_{n} = a$ then why does it exist a subsquence $s_{n}$, which $\lim_{n\to\infty} \ s_{n} = a$?

Published on 08 Dec 2015 - 18:05

score 307 · Answer 7 · 2015-12-08 22:01:22

If $\limsup|a_n|^{\frac{1}{n}} = \frac{1}{R}$ and $\frac{1}{r} > \frac{1}{R}$, why is there an $N$ such that $|a_n|^{1/n}<1/r$ for all $n\ge N$?

score 95 · Answer 8 · 2015-12-09 01:49:04

95

Views

Suppose $ \lim \left( a_{n}+a_{n+1} \right)=0 $. Show that $ \lim a_{n}=0 $ or $ 0 < \limsup a_{n} $.

Published on 09 Dec 2015 - 1:49

score 1.7k · Answer 9 · 2015-12-09 07:10:23

1.7k

Views

finding the limit superior and inferior of the sequence $\frac 1 n \cos{\frac{n\pi}{2}}$

Published on 09 Dec 2015 - 7:10

score 491 · Answer 10 · 2015-12-11 08:06:00

491

Views

Proving if $\lim|s_n|=0$ then $\limsup|s_n|=0$.

Published on 11 Dec 2015 - 8:06

score 1.7k · Answer 11 · 2015-12-15 12:42:17

1.7k

Views

Liminf and limsup of subsequences

Published on 15 Dec 2015 - 12:42

score 65 · Answer 12 · 2015-12-15 18:12:16

65

Views

Problem with $\mathbb{P}(\liminf_n(A_n\cup B_n))$

Published on 15 Dec 2015 - 18:12

score 129 · Answer 13 · 2015-12-16 04:28:26

129

Views

limit supremum that I have not seen before - for $t\to0^+$

Published on 16 Dec 2015 - 4:28

score 386 · Answer 14 · 2015-12-16 08:33:11

386

Views

Limsup of a probability

Published on 16 Dec 2015 - 8:33

score 1.5k · Answer 15 · 2015-12-20 11:08:51

1.5k

Views

liminf and limsup of events: complement

Published on 20 Dec 2015 - 11:08

List Question

Consequences of $\limsup\limits_{n \rightarrow \infty}(a_n)=1$.

Can we always find the infimum and supremum of a sequence?

If $\limsup_{n\to\infty} \ x_{n} =-\infty$ then why $\lim_{n\to\infty} \ x_{n} =-\infty$?

If $\lim_{x \to \infty} x_n = \liminf_{n \to \infty} x_n = \limsup_{n \to \infty} x_n= -\infty$ does it exist a convergent subsequence of $x_n$?

reference on limsup and liminf for functions

If $\limsup_{n\to\infty} \ x_{n} = a$ then why does it exist a subsquence $s_{n}$, which $\lim_{n\to\infty} \ s_{n} = a$?

If $\limsup|a_n|^{\frac{1}{n}} = \frac{1}{R}$ and $\frac{1}{r} > \frac{1}{R}$, why is there an $N$ such that $|a_n|^{1/n}<1/r$ for all $n\ge N$?

Suppose $ \lim \left( a_{n}+a_{n+1} \right)=0 $. Show that $ \lim a_{n}=0 $ or $ 0 < \limsup a_{n} $.

finding the limit superior and inferior of the sequence $\frac 1 n \cos{\frac{n\pi}{2}}$

Proving if $\lim|s_n|=0$ then $\limsup|s_n|=0$.

Liminf and limsup of subsequences

Problem with $\mathbb{P}(\liminf_n(A_n\cup B_n))$

limit supremum that I have not seen before - for $t\to0^+$

Limsup of a probability

liminf and limsup of events: complement

Trending Questions

Popular # Hahtags

Popular Questions