Question

How to prove If $\lim\limits_{n\to \infty}{a_{n}}^3 = a^{3}, \lim\limits_{n\to \infty} a_{n} = a$

score 110 · Answer 1 · 2018-04-17 07:11:23

110

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How to prove If $\lim\limits_{n\to \infty}{a_{n}}^3 = a^{3}, \lim\limits_{n\to \infty} a_{n} = a$

Published on 17 Apr 2018 - 7:11

score 35 · Answer 2 · 2018-04-17 14:28:28

35

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Comparison of the elements of two sequences and their distribution limits

Published on 17 Apr 2018 - 14:28

score 86 · Answer 3 · 2026-03-26 09:42:49

86

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Inconsistency of DCT and Residue theorem

Published on 26 Mar 2026 - 9:42

score 75 · Answer 4 · 2018-04-17 14:33:43

75

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$\sin x-\frac{1}{2}\sin ^2x+\frac{1}{4}\sin ^3x-\frac{1}{8}\sin ^4x....\forall x \in \mathbb{R}$ is convergent?

Published on 17 Apr 2018 - 14:33

score 254 · Answer 5 · 2018-04-17 21:47:29

254

Views

Given $f\in L^2(\mu)$, $\{f_n\}\in L^2(\mu)$, $f_n\rightarrow f$ a.e., and $\int|f_n|^2\rightarrow\int|f|^2$, then $f_n\rightarrow f$ in $L^2(\mu)$.

Published on 17 Apr 2018 - 21:47

score 81 · Answer 6 · 2018-04-18 06:38:36

81

Views

Where am I going wrong here when applying the Ratio test?

Published on 18 Apr 2018 - 6:38

score 30 · Answer 7 · 2026-03-25 03:04:01

30

Views

Definition of Convergence of a Sequence and Series Questions

Published on 25 Mar 2026 - 3:04

score 522 · Answer 8 · 2026-03-22 09:39:46

522

Views

Continued fraction rate of convergence

Published on 22 Mar 2026 - 9:39

score 256 · Answer 9 · 2026-03-25 09:44:39

256

Views

Solving linear system $Ax=b$

Published on 25 Mar 2026 - 9:44

score 190 · Answer 10 · 2026-03-25 00:02:54

190

Views

Almost sure convergence of the average of the product of 0-1 random variables

Published on 25 Mar 2026 - 0:02

score 70 · Answer 11 · 2026-03-25 04:35:27

70

Views

Completeness respect two metric.

Published on 25 Mar 2026 - 4:35

score 52 · Answer 12 · 2018-04-18 19:56:08

52

Views

How to negate $\forall\epsilon > 0,\; \exists n_0=n_0(\epsilon)\in \Bbb{N},\ni |a_n-a^{*}| <\epsilon,\;\;n\geq n_0$

Published on 18 Apr 2018 - 19:56

score 64 · Answer 13 · 2026-03-25 03:04:33

64

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Find the domain of $A(x) = 1 + \frac{x^3}{2\times3}+\frac{x^6}{2\times3\times5\times6} + \frac{x^9}{2\times3\times5\times6\times8\times9} +\space ...$

Published on 25 Mar 2026 - 3:04

score 55 · Answer 14 · 2026-03-27 12:14:27

55

Views

convergence of an improper integral, depending of a constant "a"

Published on 27 Mar 2026 - 12:14

score 253 · Answer 15 · 2018-04-19 14:19:38

253

Views

Is this sequence convergent? If so, then how to find the limit?

Published on 19 Apr 2018 - 14:19

List Question

How to prove If $\lim\limits_{n\to \infty}{a_{n}}^3 = a^{3}, \lim\limits_{n\to \infty} a_{n} = a$

Comparison of the elements of two sequences and their distribution limits

Inconsistency of DCT and Residue theorem

$\sin x-\frac{1}{2}\sin ^2x+\frac{1}{4}\sin ^3x-\frac{1}{8}\sin ^4x....\forall x \in \mathbb{R}$ is convergent?

Given $f\in L^2(\mu)$, $\{f_n\}\in L^2(\mu)$, $f_n\rightarrow f$ a.e., and $\int|f_n|^2\rightarrow\int|f|^2$, then $f_n\rightarrow f$ in $L^2(\mu)$.

Where am I going wrong here when applying the Ratio test?

Definition of Convergence of a Sequence and Series Questions

Continued fraction rate of convergence

Solving linear system $Ax=b$

Almost sure convergence of the average of the product of 0-1 random variables

Completeness respect two metric.

How to negate $\forall\epsilon > 0,\; \exists n_0=n_0(\epsilon)\in \Bbb{N},\ni |a_n-a^{*}| <\epsilon,\;\;n\geq n_0$

Find the domain of $A(x) = 1 + \frac{x^3}{2\times3}+\frac{x^6}{2\times3\times5\times6} + \frac{x^9}{2\times3\times5\times6\times8\times9} +\space ...$

convergence of an improper integral, depending of a constant "a"

Is this sequence convergent? If so, then how to find the limit?

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