List questions from sequence-of-function

Published on 16 May 2020 - 17:18

121

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If $\forall x \in (0,1] \ \ f_n(x) \to 0, n \to \infty$ then $\exists x_n \downarrow 0$ such that $f_n(x_n) \to 0$.

Published on 16 May 2020 - 21:09

45

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Geometric sequence not correct?

Published on 20 May 2020 - 6:26

206

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Let $f_n(x) = {nx\over 1+nx^2}$ on the domain $[-1,1]$

Published on 20 May 2020 - 8:05

389

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Dini's theorem (specific case)

Published on 22 May 2020 - 23:10

40

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How to show that for $p>2$ this sequence of functions is uniformly convergent?

Published on 24 May 2020 - 4:45

76

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Proving that a function sequence converges uniformly to limit function

Published on 26 May 2020 - 12:14

62

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Convergence $\sum_{k=1}^N \frac{a_k}{ \sum_{i=0}^k a_{i}^2} $

Published on 26 May 2020 - 15:01

24

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Continuity of the sequence of averages

Published on 26 May 2020 - 20:04

29

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Find a limit for a sequence of functions with the domain in $(0, \infty)$

Published on 27 May 2020 - 13:36

66

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uniform convergence of functional series $\sum_{k=1}^{\infty} {(-1)^{k} \frac{k+\sin(x)}{k^{2}}}$

Published on 28 May 2020 - 8:36

319

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Proof for uniform convergence of sequence of functions

Published on 24 Feb 2026 - 8:33

115

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Show that there exists a real number $R≥0$ such that, for all $x$, $y\in [0$, $1]$ and all $n \in \mathbb{N}$, $|g_n(x)−g_n(y)|\le R|x−y|$.

Published on 24 Feb 2026 - 8:35

35

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Find $f(x)$ to which the given sequence of functions converges

Published on 24 Feb 2026 - 8:33

74

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Is pointwise convergence permutation-invariant?

Published on 24 Feb 2026 - 8:29

List Question

How to prove that $X \cap Y$ is closed?

If $\forall x \in (0,1] \ \ f_n(x) \to 0, n \to \infty$ then $\exists x_n \downarrow 0$ such that $f_n(x_n) \to 0$.

Geometric sequence not correct?

Let $f_n(x) = {nx\over 1+nx^2}$ on the domain $[-1,1]$

Dini's theorem (specific case)

How to show that for $p>2$ this sequence of functions is uniformly convergent?

Proving that a function sequence converges uniformly to limit function

Convergence $\sum_{k=1}^N \frac{a_k}{ \sum_{i=0}^k a_{i}^2} $

Continuity of the sequence of averages

Find a limit for a sequence of functions with the domain in $(0, \infty)$

uniform convergence of functional series $\sum_{k=1}^{\infty} {(-1)^{k} \frac{k+\sin(x)}{k^{2}}}$

Proof for uniform convergence of sequence of functions

Show that there exists a real number $R≥0$ such that, for all $x$, $y\in [0$, $1]$ and all $n \in \mathbb{N}$, $|g_n(x)−g_n(y)|\le R|x−y|$.

Find $f(x)$ to which the given sequence of functions converges

Is pointwise convergence permutation-invariant?

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