Question

How can we compute $\liminf_{n→∞}(x_n+y_nz_n)$ for monotone $(x_n)_{n\in\mathbb N}$ and $(y_n)_{n\in\mathbb N}$ knowing that $\liminf_{n→∞}z_n=-1$?

score 242 · Answer 1 · 2019-03-27 20:52:41

242

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How can we compute $\liminf_{n→∞}(x_n+y_nz_n)$ for monotone $(x_n)_{n\in\mathbb N}$ and $(y_n)_{n\in\mathbb N}$ knowing that $\liminf_{n→∞}z_n=-1$?

Published on 27 Mar 2019 - 20:52

score 63 · Answer 2 · 2019-03-29 07:28:58

63

Views

Proving property of $\liminf_{x \to x_0} f(x)$

Published on 29 Mar 2019 - 7:28

score 78 · Answer 3 · 2019-03-29 16:52:18

78

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Example $f_n = \mathbf{1}_{[n,\infty)}$ in Fatou's Lemma

Published on 29 Mar 2019 - 16:52

score 93 · Answer 4 · 2019-04-02 10:05:17

93

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Given $\lim_{n \rightarrow \infty} a_n a_{n+1} = L$, how to show: $\lim_{n \rightarrow \infty} a_n a_{n+3} = L$

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score 154 · Answer 5 · 2019-04-02 19:45:37

154

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score 54 · Answer 6 · 2019-04-03 18:03:37

54

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34

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score 36 · Answer 8 · 2019-04-04 03:45:33

36

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score 42 · Answer 9 · 2019-04-08 03:12:56

42

Views

If $c_{n}=\frac{n\cos(n\pi)}{n+1}$, find $\limsup c_{n}$ and $\liminf c_{n}$.

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score 31 · Answer 10 · 2019-04-08 11:41:55

31

Views

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score 53 · Answer 11 · 2019-04-09 12:35:49

53

Views

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Published on 09 Apr 2019 - 12:35

score 108 · Answer 12 · 2019-04-11 22:25:51

108

Views

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score 182 · Answer 13 · 2019-04-20 17:25:42

182

Views

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73

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score 57 · Answer 15 · 2019-04-21 15:37:03

57

Views

Slightly alternative proof to the converse part of Cauchy's General Principle

Published on 21 Apr 2019 - 15:37

List Question

How can we compute $\liminf_{n→∞}(x_n+y_nz_n)$ for monotone $(x_n)_{n\in\mathbb N}$ and $(y_n)_{n\in\mathbb N}$ knowing that $\liminf_{n→∞}z_n=-1$?

Proving property of $\liminf_{x \to x_0} f(x)$

Example $f_n = \mathbf{1}_{[n,\infty)}$ in Fatou's Lemma

Given $\lim_{n \rightarrow \infty} a_n a_{n+1} = L$, how to show: $\lim_{n \rightarrow \infty} a_n a_{n+3} = L$

limit inferior and infimum (real analysis)

Limit sup limit inf

limit superior and inferior 2

Sequence definition of Limit Sup

If $c_{n}=\frac{n\cos(n\pi)}{n+1}$, find $\limsup c_{n}$ and $\liminf c_{n}$.

Root test of $\frac{1}{2n}$

Suppose $x_{n}>0$ and tends to zero.We know its arithmetic mean tends to zero. I wonder which will tend to zero faster.

Limit superior and inferior when one part diverges

How to change the order of the limit and the expectation?

A homework question about partial limits

Slightly alternative proof to the converse part of Cauchy's General Principle

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