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Question about a specific set inclusion

score 47 · Answer 1 · 2020-08-30 11:47:05

47

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Question about a specific set inclusion

Published on 30 Aug 2020 - 11:47

score 20 · Answer 2 · 2026-03-27 01:44:03

20

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Find converging subsequences in a metric space

Published on 27 Mar 2026 - 1:44

score 63 · Answer 3 · 2020-09-02 07:35:52

63

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can we find $ \lim_{n \to \infty}\sum_{k=1}^{n}\frac{1}{\sqrt{n^{2}+kn}} $?

Published on 02 Sep 2020 - 7:35

score 91 · Answer 4 · 2020-09-03 05:39:17

91

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how can i find $ \frac{1}{2\pi}\left ( \frac{\pi^{3}}{1!3}-\frac{\pi^{5}}{3!5}+\frac{\pi^{7}}{5!7}-... \right ) $

Published on 03 Sep 2020 - 5:39

score 277 · Answer 5 · 2020-09-04 16:43:50

277

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Let $x_n$ be a sequence of integers such that $x_{k+1}\neq x_k$ holds for every $k\ge 1$. Show that $x_n$ is not convergent.

Published on 04 Sep 2020 - 16:43

score 36 · Answer 6 · 2020-09-06 02:13:54

36

Views

$\Vert x_{n} - y_{n} \Vert $is a cauchy sequence in $\mathbb{F}$

Published on 06 Sep 2020 - 2:13

score 105 · Answer 7 · 2020-09-07 09:30:09

105

Views

Proving limits with the definition of limit

Published on 07 Sep 2020 - 9:30

score 65 · Answer 8 · 2020-09-08 23:35:08

65

Views

Order of convergence limit

Published on 08 Sep 2020 - 23:35

score 182 · Answer 9 · 2020-09-11 01:32:22

182

Views

Show that if $s_n$ converges to $\beta$, then $t_n$ converges to $\beta/2$.

Published on 11 Sep 2020 - 1:32

score 521 · Answer 10 · 2020-09-12 02:21:24

521

Views

I need help proving that Cauchy Sequences form an equivalence relation if and only if they are equivalent

Published on 12 Sep 2020 - 2:21

score 37 · Answer 11 · 2020-09-12 03:11:06

37

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Example for Cauchy construction of real numbers

Published on 12 Sep 2020 - 3:11

score 185 · Answer 12 · 2026-03-29 16:49:19

185

Views

Is the space of continuous functions on a compact set a complete space?

Published on 29 Mar 2026 - 16:49

score 38 · Answer 13 · 2020-09-12 21:43:07

38

Views

How to proof that if a sequence is Cauchy, the sequence of its norms converges?

Published on 12 Sep 2020 - 21:43

score 97 · Answer 14 · 2020-09-14 20:22:42

97

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If $a_k$ is a sequence that converges to $1/2$, prove that $b_k = 1/(1-a_k)$ is Cauchy

Published on 14 Sep 2020 - 20:22

score 95 · Answer 15 · 2020-09-14 20:29:02

95

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Proving $ \sum_{n=1}^{ \infty } f_n(1) $ converges when $ \sum_{n=1}^{ \infty } f_n(x) $ converges uniformly

Published on 14 Sep 2020 - 20:29

List Question

Question about a specific set inclusion

Find converging subsequences in a metric space

can we find $ \lim_{n \to \infty}\sum_{k=1}^{n}\frac{1}{\sqrt{n^{2}+kn}} $?

how can i find $ \frac{1}{2\pi}\left ( \frac{\pi^{3}}{1!3}-\frac{\pi^{5}}{3!5}+\frac{\pi^{7}}{5!7}-... \right ) $

Let $x_n$ be a sequence of integers such that $x_{k+1}\neq x_k$ holds for every $k\ge 1$. Show that $x_n$ is not convergent.

$\Vert x_{n} - y_{n} \Vert $is a cauchy sequence in $\mathbb{F}$

Proving limits with the definition of limit

Order of convergence limit

Show that if $s_n$ converges to $\beta$, then $t_n$ converges to $\beta/2$.

I need help proving that Cauchy Sequences form an equivalence relation if and only if they are equivalent

Example for Cauchy construction of real numbers

Is the space of continuous functions on a compact set a complete space?

How to proof that if a sequence is Cauchy, the sequence of its norms converges?

If $a_k$ is a sequence that converges to $1/2$, prove that $b_k = 1/(1-a_k)$ is Cauchy

Proving $ \sum_{n=1}^{ \infty } f_n(1) $ converges when $ \sum_{n=1}^{ \infty } f_n(x) $ converges uniformly

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