Question

Give an example of $\liminf_{k \to \infty} \frac{a_{k+1}}{a_k} \lt \liminf_{k \to \infty} (a_k)^{\frac{1}{k}}$

score 77 · Answer 1 · 2017-01-07 07:52:53

77

Views

Give an example of $\liminf_{k \to \infty} \frac{a_{k+1}}{a_k} \lt \liminf_{k \to \infty} (a_k)^{\frac{1}{k}}$

Published on 07 Jan 2017 - 7:52

score 264 · Answer 2 · 2017-01-07 22:35:55

264

Views

How to show that $\lim \sup\limits_{n \rightarrow \infty}x_n = \inf\{ a\mid \text{the set} \{ n: x_n >a\}\text{ is finite} \}$?

Published on 07 Jan 2017 - 22:35

score 334 · Answer 3 · 2017-01-10 06:49:43

334

Views

Proof that $\lim \inf \frac{u_{n+1}}{u_n} \le \lim \inf \sqrt[n]{u_n}$ for $u_n > 0$.

Published on 10 Jan 2017 - 6:49

score 896 · Answer 4 · 2017-01-11 11:07:59

896

Views

Analysis: Prove lim sup (an * bn)=lim sup (an)

Published on 11 Jan 2017 - 11:07

score 89 · Answer 5 · 2017-01-17 17:40:16

89

Views

limit superior and telescoping sequence

Published on 17 Jan 2017 - 17:40

score 134 · Answer 6 · 2017-01-18 07:59:37

134

Views

Cauchy Sequences, limes inferior, and limes superior

Published on 18 Jan 2017 - 7:59

score 654 · Answer 7 · 2017-01-21 16:45:59

654

Views

Prove that $\underline{\lim} \{a_n\}+ \underline{\lim} \{b_n\} \leq \underline{\lim} (a_n + b_n)$

Published on 21 Jan 2017 - 16:45

score 245 · Answer 8 · 2017-01-22 12:29:08

245

Views

Inferior limit of a sequence of measurable functions

Published on 22 Jan 2017 - 12:29

score 53 · Answer 9 · 2017-01-24 02:02:29

53

Views

Show that for all positive intergers $k$, $1^k+2^k+\dots+n^k=\Theta(n^{k+1})$

Published on 24 Jan 2017 - 2:02

score 832 · Answer 10 · 2017-01-26 22:43:12

832

Views

How do I prove this inequality involving $\liminf$ and $\limsup$?

Published on 26 Jan 2017 - 22:43

score 192 · Answer 11 · 2017-01-29 12:25:02

192

Views

limit superior of $\cos(x^2)-\cos[(x+1)^2]$ as $x \rightarrow \infty$

Published on 29 Jan 2017 - 12:25

score 443 · Answer 12 · 2017-01-29 19:23:26

443

Views

Proving the $\limsup\limits_{x\rightarrow\infty}x_n$ exists, using $\epsilon$ proof

Published on 29 Jan 2017 - 19:23

score 351 · Answer 13 · 2017-01-29 21:30:48

351

Views

Proving if $\limsup x_n = \liminf x_n = c$, then $x_n \rightarrow c, n \rightarrow \infty$ using $\epsilon$

Published on 29 Jan 2017 - 21:30

score 1.3k · Answer 14 · 2026-03-27 17:57:45

1.3k

Views

Inequality : Probability of infimum of a sequence of events

Published on 27 Mar 2026 - 17:57

score 75 · Answer 15 · 2017-02-03 07:49:22

75

Views

Two questions on series and limits

Published on 03 Feb 2017 - 7:49

List Question

Give an example of $\liminf_{k \to \infty} \frac{a_{k+1}}{a_k} \lt \liminf_{k \to \infty} (a_k)^{\frac{1}{k}}$

How to show that $\lim \sup\limits_{n \rightarrow \infty}x_n = \inf\{ a\mid \text{the set} \{ n: x_n >a\}\text{ is finite} \}$?

Proof that $\lim \inf \frac{u_{n+1}}{u_n} \le \lim \inf \sqrt[n]{u_n}$ for $u_n > 0$.

Analysis: Prove lim sup (an * bn)=lim sup (an)

limit superior and telescoping sequence

Cauchy Sequences, limes inferior, and limes superior

Prove that $\underline{\lim} \{a_n\}+ \underline{\lim} \{b_n\} \leq \underline{\lim} (a_n + b_n)$

Inferior limit of a sequence of measurable functions

Show that for all positive intergers $k$, $1^k+2^k+\dots+n^k=\Theta(n^{k+1})$

How do I prove this inequality involving $\liminf$ and $\limsup$?

limit superior of $\cos(x^2)-\cos[(x+1)^2]$ as $x \rightarrow \infty$

Proving the $\limsup\limits_{x\rightarrow\infty}x_n$ exists, using $\epsilon$ proof

Proving if $\limsup x_n = \liminf x_n = c$, then $x_n \rightarrow c, n \rightarrow \infty$ using $\epsilon$

Inequality : Probability of infimum of a sequence of events

Two questions on series and limits

Trending Questions

Popular # Hahtags

Popular Questions