Question

Difficulty regarding understanding a proof of multiplication of infinite series

score 393 · Answer 1 · 2026-04-10 20:05:18

393

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Difficulty regarding understanding a proof of multiplication of infinite series

Published on 10 Apr 2026 - 20:05

score 98 · Answer 2 · 2026-04-17 12:44:16

98

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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 17 Apr 2026 - 12:44

score 240 · Answer 3 · 2026-04-16 03:00:55

240

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

Published on 16 Apr 2026 - 3:00

score 153 · Answer 4 · 2026-04-14 19:13:29

153

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On the convergence of a two-sided series

Published on 14 Apr 2026 - 19:13

score 29 · Answer 5 · 2026-04-14 13:28:06

29

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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 14 Apr 2026 - 13:28

score 77 · Answer 6 · 2026-04-15 04:15:10

77

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

Published on 15 Apr 2026 - 4:15

score 38 · Answer 7 · 2026-04-11 04:57:04

38

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

Published on 11 Apr 2026 - 4:57

score 159 · Answer 8 · 2026-04-15 23:43:10

159

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

Published on 15 Apr 2026 - 23:43

score 101 · Answer 9 · 2026-04-16 09:51:18

101

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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 16 Apr 2026 - 9:51

score 43 · Answer 10 · 2026-04-15 12:34:54

43

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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 Apr 2026 - 12:34

score 331 · Answer 11 · 2026-04-08 19:43:42

331

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Help with convergence tests for series

Published on 08 Apr 2026 - 19:43

score 89 · Answer 12 · 2026-04-16 10:02:01

89

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Find the convergence radius for this power series

Published on 16 Apr 2026 - 10:02

score 116 · Answer 13 · 2026-04-09 17:55:50

116

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Convergence when ratio test=1

Published on 09 Apr 2026 - 17:55

score 164 · Answer 14 · 2026-04-12 10:16:27

164

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The proof of Taylor's theorem

Published on 12 Apr 2026 - 10:16

score 168 · Answer 15 · 2026-04-15 11:15:19

168

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

Published on 15 Apr 2026 - 11:15

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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