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First-order recursion problem with a special cubic equation: by Ji_Chen

score 122 · Answer 1 · 2026-03-26 07:38:32

122

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First-order recursion problem with a special cubic equation: by Ji_Chen

Published on 26 Mar 2026 - 7:38

score 79 · Answer 2 · 2021-02-23 09:20:32

79

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Given a recursion $a_{n+1}=\sqrt{a_n^2+a_n}$ with $a_1=1.$ Prove that $\lim{\left(a_n\right)}'=\frac12$ without using $a_n\sim\frac n2-\frac14\ln n$

Published on 23 Feb 2021 - 9:20

score 73 · Answer 3 · 2026-04-03 05:53:08

73

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Given a recursion $\frac{a_{n+1}}{4a_{n+1}+n+1}=\frac{2(a_n+n)^2}{9n(4a_n+n)}$ with $a_1=1.$ Show that $a_n\sim\frac n2\,{\rm as}\,n\rightarrow\infty$

Published on 03 Apr 2026 - 5:53

score 21 · Answer 4 · 2021-02-23 21:17:00

21

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Is n over itself, over itself ... recursively equal to one, or square-root of n?

Published on 23 Feb 2021 - 21:17

score 127 · Answer 5 · 2021-02-24 10:12:23

127

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Time complexity of a simple recurrence relation

Published on 24 Feb 2021 - 10:12

score 110 · Answer 6 · 2026-03-26 22:18:16

110

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Prove the limit equation: $\lim_{x\rightarrow\infty}e^{-x}\sum_{n=0}^{\infty}f_{n}\left(x\right)=-\gamma.$ FYI$,\quad\gamma$ is Euler's constant

Published on 26 Mar 2026 - 22:18

score 39 · Answer 7 · 2021-02-24 21:42:50

39

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Determining the closed form of a particular inhomogeneous recursive relation

Published on 24 Feb 2021 - 21:42

score 39 · Answer 8 · 2021-02-25 11:58:05

39

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Solving a problem involving primitive and partially recursive functions.

Published on 25 Feb 2021 - 11:58

score 66 · Answer 9 · 2026-04-04 16:51:34

66

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Solving the same problem in different ways obtaining different answers

Published on 04 Apr 2026 - 16:51

score 58 · Answer 10 · 2026-03-30 20:47:26

58

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Probabilistic recursion

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score 85 · Answer 11 · 2021-02-27 08:22:22

85

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Finding an exponential generating function in it's 'closed' form

Published on 27 Feb 2021 - 8:22

score 169 · Answer 12 · 2021-02-27 10:10:12

If $f$ is total recursive and $A \subseteq \Bbb N$ is recursively enumerable then $f(A), f^{-1}(A)$ are recursively enumerable.

score 37 · Answer 13 · 2026-04-06 22:12:33

37

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How to derive a model for a recursive situation

Published on 06 Apr 2026 - 22:12

score 164 · Answer 14 · 2026-04-06 10:51:45

164

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Basic questions on Turing degrees and the jump operator

Published on 06 Apr 2026 - 10:51

score 189 · Answer 15 · 2026-04-06 10:53:10

189

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The jump operator is well defined on the Turing degrees

Published on 06 Apr 2026 - 10:53

List Question

First-order recursion problem with a special cubic equation: by Ji_Chen

Given a recursion $a_{n+1}=\sqrt{a_n^2+a_n}$ with $a_1=1.$ Prove that $\lim{\left(a_n\right)}'=\frac12$ without using $a_n\sim\frac n2-\frac14\ln n$

Given a recursion $\frac{a_{n+1}}{4a_{n+1}+n+1}=\frac{2(a_n+n)^2}{9n(4a_n+n)}$ with $a_1=1.$ Show that $a_n\sim\frac n2\,{\rm as}\,n\rightarrow\infty$

Is n over itself, over itself ... recursively equal to one, or square-root of n?

Time complexity of a simple recurrence relation

Prove the limit equation: $\lim_{x\rightarrow\infty}e^{-x}\sum_{n=0}^{\infty}f_{n}\left(x\right)=-\gamma.$ FYI$,\quad\gamma$ is Euler's constant

Determining the closed form of a particular inhomogeneous recursive relation

Solving a problem involving primitive and partially recursive functions.

Solving the same problem in different ways obtaining different answers

Probabilistic recursion

Finding an exponential generating function in it's 'closed' form

If $f$ is total recursive and $A \subseteq \Bbb N$ is recursively enumerable then $f(A), f^{-1}(A)$ are recursively enumerable.

How to derive a model for a recursive situation

Basic questions on Turing degrees and the jump operator

The jump operator is well defined on the Turing degrees

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