Question

How to calculate $\lim\frac{x_n}{y_n}$ where $0<x_0<y_0<\frac{\pi}{2}$ and $x_{n+1}=\sin{x_n}, y_{n+1}=\sin{y_n}$?

score 207 · Answer 1 · 2026-05-15 14:40:09

207

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How to calculate $\lim\frac{x_n}{y_n}$ where $0<x_0<y_0<\frac{\pi}{2}$ and $x_{n+1}=\sin{x_n}, y_{n+1}=\sin{y_n}$?

Published on 15 May 2026 - 14:40

score 349 · Answer 2 · 2026-05-11 06:55:30

349

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Trying to find a closed form summation related to Poisson distribution

Published on 11 May 2026 - 6:55

score 458 · Answer 3 · 2026-05-15 14:38:34

458

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Finding lim sup and lim inf of a recursive sequence

Published on 15 May 2026 - 14:38

score 103 · Answer 4 · 2026-05-14 15:06:43

103

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Series of the form $\sum \frac {1}{{p_k}^n}$

Published on 14 May 2026 - 15:06

score 593 · Answer 5 · 2026-04-16 09:54:44

593

Views

Sum of two sequences converges and one of them is bounded implies they both converge

Published on 16 Apr 2026 - 9:54

score 96 · Answer 6 · 2026-05-13 23:06:02

96

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Convergence of a real sequence (stochastic approximation)

Published on 13 May 2026 - 23:06

score 110 · Answer 7 · 2026-04-11 15:29:53

110

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Is a closed form of this sum possible?

Published on 11 Apr 2026 - 15:29

score 42 · Answer 8 · 2026-05-15 14:37:41

42

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Can the following limits be zero?

Published on 15 May 2026 - 14:37

score 137 · Answer 9 · 2026-04-15 16:44:54

137

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Convergence of $\sum_{n=1}^{\infty}\left(\frac{\sin(2\alpha^n)}{\alpha^n}-2\right)$

Published on 15 Apr 2026 - 16:44

score 53 · Answer 10 · 2026-04-15 15:25:53

Does the series $ \ \sum_{n=1}^{\infty} (-1)^{n-1} \frac{x^2+n^2}{n^3} $ converges uniformly on $ \ \ \ [-1,1] \ $?

score 134 · Answer 11 · 2026-04-17 03:28:44

134

Views

Let $a_n \neq 0 \;\; \forall n \in \mathbb{N}$ and $\exists L = \lim |\frac{a_{n+1}}{a_n}|$. Show that, if $L<1$, then $\lim a_n = 0$

Published on 17 Apr 2026 - 3:28

score 954 · Answer 12 · 2026-05-15 03:10:34

954

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uniform convergence $\sum _{n=0} ^{\infty} \frac{\log (1+nx)}{nx^n}$ on $x \in (1,\infty)$

Published on 15 May 2026 - 3:10

score 1.1k · Answer 13 · 2026-04-12 16:17:29

1.1k

Views

Convergence/Divergence of an Infinite Series with Natural Logarithms

Published on 12 Apr 2026 - 16:17

score 234 · Answer 14 · 2026-04-14 10:45:38

234

Views

Proof by induction that you can order natural numbers where the average isn't between any pair of numbers

Published on 14 Apr 2026 - 10:45

score 880 · Answer 15 · 2026-05-14 10:24:28

880

Views

Summation of Double Exponential Series

Published on 14 May 2026 - 10:24

List Question

How to calculate $\lim\frac{x_n}{y_n}$ where $0<x_0<y_0<\frac{\pi}{2}$ and $x_{n+1}=\sin{x_n}, y_{n+1}=\sin{y_n}$?

Trying to find a closed form summation related to Poisson distribution

Finding lim sup and lim inf of a recursive sequence

Series of the form $\sum \frac {1}{{p_k}^n}$

Sum of two sequences converges and one of them is bounded implies they both converge

Convergence of a real sequence (stochastic approximation)

Is a closed form of this sum possible?

Can the following limits be zero?

Convergence of $\sum_{n=1}^{\infty}\left(\frac{\sin(2\alpha^n)}{\alpha^n}-2\right)$

Does the series $ \ \sum_{n=1}^{\infty} (-1)^{n-1} \frac{x^2+n^2}{n^3} $ converges uniformly on $ \ \ \ [-1,1] \ $?

Let $a_n \neq 0 \;\; \forall n \in \mathbb{N}$ and $\exists L = \lim |\frac{a_{n+1}}{a_n}|$. Show that, if $L<1$, then $\lim a_n = 0$

uniform convergence $\sum _{n=0} ^{\infty} \frac{\log (1+nx)}{nx^n}$ on $x \in (1,\infty)$

Convergence/Divergence of an Infinite Series with Natural Logarithms

Proof by induction that you can order natural numbers where the average isn't between any pair of numbers

Summation of Double Exponential Series

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