Question

Difficulty regarding understanding a proof of multiplication of infinite series

score 390 · Answer 1 · 2018-12-27 14:36:20

390

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Difficulty regarding understanding a proof of multiplication of infinite series

Published on 27 Dec 2018 - 14:36

score 95 · Answer 2 · 2018-12-28 15:31:44

95

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Hint requested for: If $\sum_{n=0}^{\infty} a_n x^n$ converges for some $x_0$, then it converges uniformly and absolutely on $[-a, a]$ with $a<|x_0|$?

Published on 28 Dec 2018 - 15:31

score 237 · Answer 3 · 2018-12-31 17:32:43

237

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Let $X$ be a Banach space then every absolutely convergent series in $X$ converges in $X$

Published on 31 Dec 2018 - 17:32

score 150 · Answer 4 · 2019-01-03 05:56:49

150

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On the convergence of a two-sided series

Published on 03 Jan 2019 - 5:56

score 26 · Answer 5 · 2019-01-04 12:04:52

26

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absolut and uniform convergence of complex power series on an open disk imply absolut and local uniform convergence on the whole disk of convergence

Published on 04 Jan 2019 - 12:04

score 75 · Answer 6 · 2019-01-21 20:29:53

75

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If $a_n$ doesn't have any subsequence that converges, can $|a_n|$ converge?

Published on 21 Jan 2019 - 20:29

score 35 · Answer 7 · 2019-01-29 07:26:28

35

Views

Convergence of $a_k=\sum_{k=5}^{+\infty}(-1)^k({3\over2})^{-k}(k^2+5)\sin(k+5)$

Published on 29 Jan 2019 - 7:26

score 156 · Answer 8 · 2019-02-07 16:27:34

156

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Concluding whether $(y_n)_n$ is a bounded sequence

Published on 07 Feb 2019 - 16:27

score 98 · Answer 9 · 2019-02-13 04:38:12

98

Views

About $f(x) = \sum_{x_n < x} c_n$ in Remark 4.31 on p.97 in "Principles of Mathematical Analysis 3rd Edition" by Walter Rudin.

Published on 13 Feb 2019 - 4:38

score 40 · Answer 10 · 2019-02-15 00:19:46

40

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Prove that $\sum_{i \in S} c_i \leq \sum_{i \in S'} c_i$ if $S \subset S' \subset \mathbb{N}$.

Published on 15 Feb 2019 - 0:19

score 328 · Answer 11 · 2019-02-16 14:58:00

328

Views

Help with convergence tests for series

Published on 16 Feb 2019 - 14:58

score 86 · Answer 12 · 2019-02-18 04:36:12

86

Views

Find the convergence radius for this power series

Published on 18 Feb 2019 - 4:36

score 113 · Answer 13 · 2019-02-26 20:01:31

113

Views

Convergence when ratio test=1

Published on 26 Feb 2019 - 20:01

score 161 · Answer 14 · 2019-02-27 02:47:42

161

Views

The proof of Taylor's theorem

Published on 27 Feb 2019 - 2:47

score 165 · Answer 15 · 2019-03-02 18:57:07

165

Views

If every rearrangement of the series converges uniformly then the series converges absolutely uniformly

Published on 02 Mar 2019 - 18:57

List Question

Difficulty regarding understanding a proof of multiplication of infinite series

Hint requested for: If $\sum_{n=0}^{\infty} a_n x^n$ converges for some $x_0$, then it converges uniformly and absolutely on $[-a, a]$ with $a<|x_0|$?

Let $X$ be a Banach space then every absolutely convergent series in $X$ converges in $X$

On the convergence of a two-sided series

absolut and uniform convergence of complex power series on an open disk imply absolut and local uniform convergence on the whole disk of convergence

If $a_n$ doesn't have any subsequence that converges, can $|a_n|$ converge?

Convergence of $a_k=\sum_{k=5}^{+\infty}(-1)^k({3\over2})^{-k}(k^2+5)\sin(k+5)$

Concluding whether $(y_n)_n$ is a bounded sequence

About $f(x) = \sum_{x_n < x} c_n$ in Remark 4.31 on p.97 in "Principles of Mathematical Analysis 3rd Edition" by Walter Rudin.

Prove that $\sum_{i \in S} c_i \leq \sum_{i \in S'} c_i$ if $S \subset S' \subset \mathbb{N}$.

Help with convergence tests for series

Find the convergence radius for this power series

Convergence when ratio test=1

The proof of Taylor's theorem

If every rearrangement of the series converges uniformly then the series converges absolutely uniformly

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