Question

Convergence of $a_n=\sum\limits_{m=2}^{n} \frac{(-1)^mm}{(\ln(m))^m}$ and $b_n = \sum\limits_{m=2}^{n} \frac{1}{(\ln(m))^m}$

score 227 · Answer 1 · 2019-02-20 09:03:53

227

Views

Convergence of $a_n=\sum\limits_{m=2}^{n} \frac{(-1)^mm}{(\ln(m))^m}$ and $b_n = \sum\limits_{m=2}^{n} \frac{1}{(\ln(m))^m}$

Published on 20 Feb 2019 - 9:03

score 871 · Answer 2 · 2019-02-20 12:33:36

871

Views

Greatest lower bound of the set : $\{(e^n + 2^n)^\frac1n\ | \; n\in \mathbb{N}\}$

Published on 20 Feb 2019 - 12:33

score 71 · Answer 3 · 2019-02-21 13:59:47

71

Views

If $a_n=n\left(1-\frac{1}{n}\right)^{n[\log n]}$, prove $1\leqslant \liminf a_n$ and $\limsup a_n\leqslant e.$

Published on 21 Feb 2019 - 13:59

score 327 · Answer 4 · 2019-02-22 16:41:07

327

Views

Is it possible to find $\limsup\limits_{n\to\infty} \frac{2×3^n-3×2^n}{2^{\alpha(n)}-3^n}$?

Published on 22 Feb 2019 - 16:41

score 958 · Answer 5 · 2019-02-23 18:59:41

958

Views

$\lim$ vs $\liminf$ and $\limsup$ in the proof of convergence in probability implies convergence in distribution

Published on 23 Feb 2019 - 18:59

score 71 · Answer 6 · 2019-02-23 21:58:18

71

Views

Very challenging measure theory problem with $L^p$ norms and lower bound for probability

Published on 23 Feb 2019 - 21:58

score 522 · Answer 7 · 2019-02-28 15:20:36

522

Views

What does this notation mean: $\limsup_{\epsilon \to 0} \dots$

Published on 28 Feb 2019 - 15:20

score 329 · Answer 8 · 2019-03-03 04:04:13

329

Views

Set sequences $\liminf$ and $\limsup$ - correct?

Published on 03 Mar 2019 - 4:04

score 1.1k · Answer 9 · 2019-03-07 12:03:28

1.1k

Views

Finding the lim inf and lim sup of a sequence

Published on 07 Mar 2019 - 12:03

score 69 · Answer 10 · 2019-03-17 10:57:00

69

Views

How to evaluate $\lim_{N\to\infty}\sup_{x\in(1,\infty)}\big|\sum_{n=N+1}^{\infty}\frac{1}{1+x^n}\big|$?

Published on 17 Mar 2019 - 10:57

score 74 · Answer 11 · 2019-03-20 21:56:36

74

Views

Can we conclude $\liminf_{n\to\infty}\operatorname E\left[1\wedge e^{X_n}\right]=0$ from $\liminf_{n\to\infty}X_n=-\infty$?

Published on 20 Mar 2019 - 21:56

score 324 · Answer 12 · 2026-03-25 22:09:18

324

Views

Problem to understand Borel-Cantelli Lemma

Published on 25 Mar 2026 - 22:09

score 90 · Answer 13 · 2019-03-24 20:22:54

90

Views

Logical proof for independent sequence of sets

Published on 24 Mar 2019 - 20:22

score 668 · Answer 14 · 2019-03-25 10:40:28

668

Views

Suppose $(a_n)^{n\to\infty}_{n=1}$ is a bounded sequence of real numbers. Prove that: $\liminf a_n \leq\limsup a_n$

Published on 25 Mar 2019 - 10:40

score 42 · Answer 15 · 2019-03-27 03:18:37

42

Views

Question about lim inf or lim sup

Published on 27 Mar 2019 - 3:18

List Question

Convergence of $a_n=\sum\limits_{m=2}^{n} \frac{(-1)^mm}{(\ln(m))^m}$ and $b_n = \sum\limits_{m=2}^{n} \frac{1}{(\ln(m))^m}$

Greatest lower bound of the set : $\{(e^n + 2^n)^\frac1n\ | \; n\in \mathbb{N}\}$

If $a_n=n\left(1-\frac{1}{n}\right)^{n[\log n]}$, prove $1\leqslant \liminf a_n$ and $\limsup a_n\leqslant e.$

Is it possible to find $\limsup\limits_{n\to\infty} \frac{2×3^n-3×2^n}{2^{\alpha(n)}-3^n}$?

$\lim$ vs $\liminf$ and $\limsup$ in the proof of convergence in probability implies convergence in distribution

Very challenging measure theory problem with $L^p$ norms and lower bound for probability

What does this notation mean: $\limsup_{\epsilon \to 0} \dots$

Set sequences $\liminf$ and $\limsup$ - correct?

Finding the lim inf and lim sup of a sequence

How to evaluate $\lim_{N\to\infty}\sup_{x\in(1,\infty)}\big|\sum_{n=N+1}^{\infty}\frac{1}{1+x^n}\big|$?

Can we conclude $\liminf_{n\to\infty}\operatorname E\left[1\wedge e^{X_n}\right]=0$ from $\liminf_{n\to\infty}X_n=-\infty$?

Problem to understand Borel-Cantelli Lemma

Logical proof for independent sequence of sets

Suppose $(a_n)^{n\to\infty}_{n=1}$ is a bounded sequence of real numbers. Prove that: $\liminf a_n \leq\limsup a_n$

Question about lim inf or lim sup

Trending Questions

Popular # Hahtags

Popular Questions