Question

Example of a sequence such that $(n^2(a_n-a_{n+2} -(a_{n+2} -a_{n+4})))$ is bounded but $(n^2(a_n-a_{n+2}))$ is not bounded

score 52 · Answer 1 · 2023-09-13 21:05:38

52

Views

Example of a sequence such that $(n^2(a_n-a_{n+2} -(a_{n+2} -a_{n+4})))$ is bounded but $(n^2(a_n-a_{n+2}))$ is not bounded

Published on 13 Sep 2023 - 21:05

score 29 · Answer 2 · 2023-09-16 16:04:37

29

Views

Existence of Bound of Width $\epsilon$ for Non-Cauchy Rational Sequence

Published on 16 Sep 2023 - 16:04

score 23 · Answer 3 · 2023-09-17 10:35:50

23

Views

Showing that $(XY_n)$ is a Cauchy sequence when $(Y_n)$ is cauchy in space of polynomias.

Published on 17 Sep 2023 - 10:35

score 84 · Answer 4 · 2023-09-19 14:06:06

84

Views

Sol Verif: Prove that if $\lim_{n \rightarrow \infty }\sum u_n=l\Rightarrow \lim_{n \rightarrow \infty} u_n=0$ via Cauchy

Published on 19 Sep 2023 - 14:06

score 22 · Answer 5 · 2023-09-21 10:57:07

22

Views

Prove the Cauchy Convergence for Brachystochrone

Published on 21 Sep 2023 - 10:57

score 33 · Answer 6 · 2023-09-27 06:38:26

33

Views

If $s_n$ is a sequence that converges, then show that if $s_n \ge a$ for all but finitely many $n$, then $\lim s_n \ge a$

Published on 27 Sep 2023 - 6:38

score 82 · Answer 7 · 2023-09-27 11:02:30

82

Views

Extracting pointwise convergent subsequence. Is my proof correct?

Published on 27 Sep 2023 - 11:02

score 44 · Answer 8 · 2023-09-28 12:16:24

44

Views

Confusing notation of sequences in $k$-dimensional Euclidean spaces.

Published on 28 Sep 2023 - 12:16

score 26 · Answer 9 · 2023-09-30 06:31:57

26

Views

Symbolizing Definition of Cauchy Sequence with Predicate Logic

Published on 30 Sep 2023 - 6:31

score 91 · Answer 10 · 2023-10-01 16:00:22

91

Views

How to check the convergence or divergence of sequence $\sqrt{3},\sqrt{3\sqrt{3}},\sqrt{\sqrt{3}\sqrt{3}},\dots$?

Published on 01 Oct 2023 - 16:00

score 151 · Answer 11 · 2023-10-04 12:00:45

151

Views

What is the difference between this alternate definition of Cauchy and its actual definition? Will this one work?

Published on 04 Oct 2023 - 12:00

score 85 · Answer 12 · 2026-03-27 17:57:34

85

Views

Show that $C([0, 1])$ equipped with $\Vert f\Vert_1:=\int_0^1|f(x)|dx$ is not complete

Published on 27 Mar 2026 - 17:57

score 54 · Answer 13 · 2023-10-06 12:11:17

54

Views

if (un) be a monotone bounded sequence, prove that exactly one of l.u.b and g.l.b. of (un) does not belong to (un)

Published on 06 Oct 2023 - 12:11

score 50 · Answer 14 · 2023-10-07 22:09:34

50

Views

Doubt about continuity of a function

Published on 07 Oct 2023 - 22:09

score 71 · Answer 15 · 2026-03-27 17:53:08

71

Views

In a complete space $X$ is every $x \in X$ the limit of a sequence $\{x_n\}$ such that $x \not\in \{x_n\}$?

Published on 27 Mar 2026 - 17:53

List Question

Example of a sequence such that $(n^2(a_n-a_{n+2} -(a_{n+2} -a_{n+4})))$ is bounded but $(n^2(a_n-a_{n+2}))$ is not bounded

Existence of Bound of Width $\epsilon$ for Non-Cauchy Rational Sequence

Showing that $(XY_n)$ is a Cauchy sequence when $(Y_n)$ is cauchy in space of polynomias.

Sol Verif: Prove that if $\lim_{n \rightarrow \infty }\sum u_n=l\Rightarrow \lim_{n \rightarrow \infty} u_n=0$ via Cauchy

Prove the Cauchy Convergence for Brachystochrone

If $s_n$ is a sequence that converges, then show that if $s_n \ge a$ for all but finitely many $n$, then $\lim s_n \ge a$

Extracting pointwise convergent subsequence. Is my proof correct?

Confusing notation of sequences in $k$-dimensional Euclidean spaces.

Symbolizing Definition of Cauchy Sequence with Predicate Logic

How to check the convergence or divergence of sequence $\sqrt{3},\sqrt{3\sqrt{3}},\sqrt{\sqrt{3}\sqrt{3}},\dots$?

What is the difference between this alternate definition of Cauchy and its actual definition? Will this one work?

Show that $C([0, 1])$ equipped with $\Vert f\Vert_1:=\int_0^1|f(x)|dx$ is not complete

if (un) be a monotone bounded sequence, prove that exactly one of l.u.b and g.l.b. of (un) does not belong to (un)

Doubt about continuity of a function

In a complete space $X$ is every $x \in X$ the limit of a sequence $\{x_n\}$ such that $x \not\in \{x_n\}$?

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