List questions from convergence-divergence

Published on 13 Apr 2026 - 14:39

125

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Does a sequence $a_n$ converge if $|a_n-\frac{1}{n} \sum_{i=1}^n a_i| \to 0$, as $n \to \infty$?

Published on 16 Apr 2026 - 9:32

82

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question about convergence and divergence of $\sum (n-2)^3\,e^{-n(x+2)}$

Published on 16 Apr 2026 - 6:28

177

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Any convergent sequence is bounded. Don’t we need to use the absolute value in this proof?

Published on 15 Apr 2026 - 13:20

166

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Calculating $\lim\limits_{n\to\infty}\frac{1+2+3+...+n-1}{n^2}$

Published on 25 Mar 2026 - 23:16

157

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How can we prove that this integral converges?

Published on 14 Apr 2026 - 7:02

50

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Example of a sequence needed that satisfies certain conditions

Published on 12 Apr 2026 - 5:22

67

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Determine that if $a_n \longrightarrow L$ then $\sqrt[n]{a_1\cdot...a_n}\longrightarrow L$

Published on 25 Mar 2026 - 23:11

89

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Proving $\displaystyle{\lim _{n\to\infty}}\sqrt[n]{n} = 1$ given that $\inf \{\sqrt[n]{n}|n\in \mathbb{N}\} = 1$

Published on 25 Mar 2026 - 23:11

117

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Prove $O\left(\frac{1}{T}\right)$ convergence rate

Published on 17 Apr 2026 - 3:43

324

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Convergence in measure is the equivalent with convergence in metric

Published on 11 Apr 2026 - 0:51

51

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Does Fourier imply Laplace?

Published on 09 Apr 2026 - 20:30

175

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Every third term alternates and I need to find if it converges.

Published on 12 Apr 2026 - 20:58

56

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Intuitively, $\sqrt{n}$ is not convergent. However, $|\sqrt{n+p}-\sqrt{n}|<\epsilon, \forall \epsilon>0, p\geq 1$

Published on 16 Apr 2026 - 3:43

176

Views

Showing $h_n$ does not uniformly converge

Published on 11 Apr 2026 - 14:48

List Question

Proof finite dimensional equaltiy implies equality on interval

Does a sequence $a_n$ converge if $|a_n-\frac{1}{n} \sum_{i=1}^n a_i| \to 0$, as $n \to \infty$?

question about convergence and divergence of $\sum (n-2)^3\,e^{-n(x+2)}$

Any convergent sequence is bounded. Don’t we need to use the absolute value in this proof?

Calculating $\lim\limits_{n\to\infty}\frac{1+2+3+...+n-1}{n^2}$

How can we prove that this integral converges?

Example of a sequence needed that satisfies certain conditions

Determine that if $a_n \longrightarrow L$ then $\sqrt[n]{a_1\cdot...a_n}\longrightarrow L$

Proving $\displaystyle{\lim _{n\to\infty}}\sqrt[n]{n} = 1$ given that $\inf \{\sqrt[n]{n}|n\in \mathbb{N}\} = 1$

Prove $O\left(\frac{1}{T}\right)$ convergence rate

Convergence in measure is the equivalent with convergence in metric

Does Fourier imply Laplace?

Every third term alternates and I need to find if it converges.

Intuitively, $\sqrt{n}$ is not convergent. However, $|\sqrt{n+p}-\sqrt{n}|<\epsilon, \forall \epsilon>0, p\geq 1$

Showing $h_n$ does not uniformly converge

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