Question

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

score 128 · Answer 1 · 2026-05-07 11:32:54

128

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

Published on 07 May 2026 - 11:32

score 497 · Answer 2 · 2026-05-02 20:03:22

497

Views

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 02 May 2026 - 20:03

score 3.5k · Answer 3 · 2026-04-29 12:32:11

3.5k

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$\liminf, \limsup$ and continuous functions

Published on 29 Apr 2026 - 12:32

score 141 · Answer 4 · 2026-04-29 12:27:54

141

Views

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

Published on 29 Apr 2026 - 12:27

score 107 · Answer 5 · 2026-05-02 23:53:03

107

Views

A question on the liminf of a sequence

Published on 02 May 2026 - 23:53

score 218 · Answer 6 · 2026-04-29 12:32:14

218

Views

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

Published on 29 Apr 2026 - 12:32

score 53 · Answer 7 · 2026-05-06 02:21:50

53

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Inferior limit when t decreases to 0

Published on 06 May 2026 - 2:21

score 1.1k · Answer 8 · 2026-05-07 07:42:11

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 07 May 2026 - 7:42

score 211 · Answer 9 · 2026-04-25 03:07:29

211

Views

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

Published on 25 Apr 2026 - 3:07

score 125 · Answer 10 · 2026-05-07 17:21:20

125

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 07 May 2026 - 17:21

score 100 · Answer 11 · 2026-04-29 12:32:12

100

Views

Extrema of this sequence

Published on 29 Apr 2026 - 12:32

score 1.1k · Answer 12 · 2026-04-23 11:56:48

1.1k

Views

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

Published on 23 Apr 2026 - 11:56

score 68 · Answer 13 · 2026-04-23 11:55:22

68

Views

series of products of two sequences

Published on 23 Apr 2026 - 11:55

score 97 · Answer 14 · 2026-04-23 11:56:11

97

Views

Evaluating the liminf and limsup

Published on 23 Apr 2026 - 11:56

score 67 · Answer 15 · 2026-04-23 11:56:48

67

Views

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

Published on 23 Apr 2026 - 11:56

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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