Question

$\alpha$ is an irrational number. Is $\liminf_{n\rightarrow\infty}n\{ n\alpha\}$ always positive?

score 117 · Answer 1 · 2026-03-17 13:24:15

117

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$\alpha$ is an irrational number. Is $\liminf_{n\rightarrow\infty}n\{ n\alpha\}$ always positive?

Published on 17 Mar 2026 - 13:24

score 489 · Answer 2 · 2026-03-22 12:00:58

489

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Prove that $\lim_{n\to \infty} (a_1a_2\ldots a_n)^{\frac 1n} = L$ given that $\lim_{n\to \infty} (a_n) = L$

Published on 22 Mar 2026 - 12:00

score 3.5k · Answer 3 · 2026-03-20 12:15:58

3.5k

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$\liminf, \limsup$ and continuous functions

Published on 20 Mar 2026 - 12:15

score 135 · Answer 4 · 2026-03-20 07:25:37

135

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Maximum and Minimum value of function -8x^2 -3 at interval (-inf, +inf)

Published on 20 Mar 2026 - 7:25

score 96 · Answer 5 · 2026-03-24 08:42:42

96

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A question on the liminf of a sequence

Published on 24 Mar 2026 - 8:42

score 212 · Answer 6 · 2026-03-22 07:14:29

212

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connection between $\limsup[a_n, b_n]$ and $[\limsup a_n, \limsup b_n]$

Published on 22 Mar 2026 - 7:14

score 42 · Answer 7 · 2026-03-22 17:41:33

42

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Inferior limit when t decreases to 0

Published on 22 Mar 2026 - 17:41

score 1.1k · Answer 8 · 2026-03-22 08:48:06

1.1k

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Trying to figure out $\mu(\liminf_{n\to \infty}A_n) \le \liminf_{n\to \infty}\mu(A_n)$

Published on 22 Mar 2026 - 8:48

score 205 · Answer 9 · 2026-03-22 09:07:19

205

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$\lim \sup_{t\rightarrow \infty} \frac{W_t}{\sqrt{t}}$ question

Published on 22 Mar 2026 - 9:07

score 116 · Answer 10 · 2026-03-23 02:54:01

116

Views

If $(a_{n})_{n}$ is a bounded sequence, show that $\liminf_{n\to \infty}a_{n}\leq \liminf_{n\to \infty}\frac{a_{1}+a_{2}+\cdots +a_{n}}{n}$.

Published on 23 Mar 2026 - 2:54

score 94 · Answer 11 · 2026-03-20 07:46:13

94

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Extrema of this sequence

Published on 20 Mar 2026 - 7:46

score 1.1k · Answer 12 · 2026-03-23 06:30:27

1.1k

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$\lim \sup$ and $\lim \inf$ of root and ratio test sequences of a series (Rudin)

Published on 23 Mar 2026 - 6:30

score 59 · Answer 13 · 2026-03-17 00:13:21

59

Views

series of products of two sequences

Published on 17 Mar 2026 - 0:13

score 90 · Answer 14 · 2026-03-22 18:48:15

90

Views

Evaluating the liminf and limsup

Published on 22 Mar 2026 - 18:48

score 60 · Answer 15 · 2026-03-23 11:58:53

60

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Upper limit of an indicator and indicator of an upper limit of sets

Published on 23 Mar 2026 - 11:58

List Question

$\alpha$ is an irrational number. Is $\liminf_{n\rightarrow\infty}n\{ n\alpha\}$ always positive?

Prove that $\lim_{n\to \infty} (a_1a_2\ldots a_n)^{\frac 1n} = L$ given that $\lim_{n\to \infty} (a_n) = L$

$\liminf, \limsup$ and continuous functions

Maximum and Minimum value of function -8x^2 -3 at interval (-inf, +inf)

A question on the liminf of a sequence

connection between $\limsup[a_n, b_n]$ and $[\limsup a_n, \limsup b_n]$

Inferior limit when t decreases to 0

Trying to figure out $\mu(\liminf_{n\to \infty}A_n) \le \liminf_{n\to \infty}\mu(A_n)$

$\lim \sup_{t\rightarrow \infty} \frac{W_t}{\sqrt{t}}$ question

If $(a_{n})_{n}$ is a bounded sequence, show that $\liminf_{n\to \infty}a_{n}\leq \liminf_{n\to \infty}\frac{a_{1}+a_{2}+\cdots +a_{n}}{n}$.

Extrema of this sequence

$\lim \sup$ and $\lim \inf$ of root and ratio test sequences of a series (Rudin)

series of products of two sequences

Evaluating the liminf and limsup

Upper limit of an indicator and indicator of an upper limit of sets

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