Question

Almost sure convergence of $|X_n|/n$ for a sequence of i.i.d r.v.'s

score 2.5k · Answer 1 · 2026-03-25 14:24:35

2.5k

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Almost sure convergence of $|X_n|/n$ for a sequence of i.i.d r.v.'s

Published on 25 Mar 2026 - 14:24

score 91 · Answer 2 · 2026-03-29 03:36:23

91

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For what $x>0$ series $\sum_{n=1}^{\infty} x^{1+\frac{1}{\sqrt2}+\frac{1}{\sqrt3}...+\frac{1}{\sqrt n}}$ is convergent?

Published on 29 Mar 2026 - 3:36

score 50 · Answer 3 · 2026-03-28 18:17:12

50

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Prove $(1+\frac{x}{n})^n$ converges for all $x \in R$

Published on 28 Mar 2026 - 18:17

score 64 · Answer 4 · 2018-11-14 07:51:15

64

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How often will $a_{n+1}=|a_n|^p\sin a_n$ tend to $0$?

Published on 14 Nov 2018 - 7:51

score 106 · Answer 5 · 2026-02-23 04:19:04

106

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construction of step functions to show integrability using Beppo Levi's theorem

Published on 23 Feb 2026 - 4:19

score 817 · Answer 6 · 2018-11-14 08:57:57

817

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Let $Y ∼ U[0, 1]$, and let $X_n = Y^n$. Prove that $X_n\to 0$ in probability.

Published on 14 Nov 2018 - 8:57

score 25 · Answer 7 · 2026-03-29 18:29:36

25

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Solving a linked recurrent relations

Published on 29 Mar 2026 - 18:29

score 346 · Answer 8 · 2018-11-14 16:13:54

346

Views

Convergence and divergence of series when changing finite number of summands

Published on 14 Nov 2018 - 16:13

score 308 · Answer 9 · 2026-03-25 13:54:41

308

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Absolutely convergent series of complex functions.

Published on 25 Mar 2026 - 13:54

score 3k · Answer 10 · 2018-11-14 19:10:22

3k

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Does this sequence $a(n) = \frac{1}{n^3\sin(n)}$ converge

Published on 14 Nov 2018 - 19:10

score 102 · Answer 11 · 2018-11-15 05:58:37

102

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Sum of the series $\sum_{n=1}^\infty n^2e^{{-(\log n)}^{1+\delta}}$ for some $\delta > 0$.

Published on 15 Nov 2018 - 5:58

score 179 · Answer 12 · 2026-03-29 18:31:08

179

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Prove that a sequence give by a recurrence relation converges

Published on 29 Mar 2026 - 18:31

score 65 · Answer 13 · 2026-03-25 14:25:57

65

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For random variables $(X_k)_{k=1}^\infty$ in $\mathbb{R}$, find $(c_k)_{k=1}^\infty$ such that $P(\lim (X_k/c_k)=0)$

Published on 25 Mar 2026 - 14:25

score 60 · Answer 14 · 2018-11-15 12:53:20

60

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If we can derive that $\{x_{f(n)+1}\}$ converges to $a$ from that $\{x_{f(n)+1}\}$converges to $a$

Published on 15 Nov 2018 - 12:53

score 535 · Answer 15 · 2018-11-15 14:39:23

535

Views

Dealing with $\sin$ and $\cos$ in a series

Published on 15 Nov 2018 - 14:39

List Question

Almost sure convergence of $|X_n|/n$ for a sequence of i.i.d r.v.'s

For what $x>0$ series $\sum_{n=1}^{\infty} x^{1+\frac{1}{\sqrt2}+\frac{1}{\sqrt3}...+\frac{1}{\sqrt n}}$ is convergent?

Prove $(1+\frac{x}{n})^n$ converges for all $x \in R$

How often will $a_{n+1}=|a_n|^p\sin a_n$ tend to $0$?

construction of step functions to show integrability using Beppo Levi's theorem

Let $Y ∼ U[0, 1]$, and let $X_n = Y^n$. Prove that $X_n\to 0$ in probability.

Solving a linked recurrent relations

Convergence and divergence of series when changing finite number of summands

Absolutely convergent series of complex functions.

Does this sequence $a(n) = \frac{1}{n^3\sin(n)}$ converge

Sum of the series $\sum_{n=1}^\infty n^2e^{{-(\log n)}^{1+\delta}}$ for some $\delta > 0$.

Prove that a sequence give by a recurrence relation converges

For random variables $(X_k)_{k=1}^\infty$ in $\mathbb{R}$, find $(c_k)_{k=1}^\infty$ such that $P(\lim (X_k/c_k)=0)$

If we can derive that $\{x_{f(n)+1}\}$ converges to $a$ from that $\{x_{f(n)+1}\}$converges to $a$

Dealing with $\sin$ and $\cos$ in a series

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