Question

Prove an algorithm for logarithmic mean $\lim_{n \to \infty} a_n=\lim_{n \to \infty} b_n=\frac{a_0-b_0}{\ln a_0-\ln b_0}$

score 206 · Answer 1 · 2026-04-16 07:27:20

206

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Prove an algorithm for logarithmic mean $\lim_{n \to \infty} a_n=\lim_{n \to \infty} b_n=\frac{a_0-b_0}{\ln a_0-\ln b_0}$

Published on 16 Apr 2026 - 7:27

score 129 · Answer 2 · 2026-04-17 12:36:58

129

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The sequence $(a_n)$ is given as $a_1=1, a_{2n} = a_n - 1, a_{2n+1} = a_n + 1$. $a_{2015}=$?

Published on 17 Apr 2026 - 12:36

score 38 · Answer 3 · 2026-04-13 00:49:29

38

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limiting point of a difference equation with coefficients related to a characteristic polynomial

Published on 13 Apr 2026 - 0:49

score 106 · Answer 4 · 2026-04-01 14:35:59

106

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Find the $m$ such $a_{n+1}=a^5_{n}+487$

Published on 01 Apr 2026 - 14:35

score 430 · Answer 5 · 2026-04-17 13:03:30

430

Views

Limit of the sequence $a_{n+1}=\frac{1}{2} (a_n+\sqrt{\frac{a_n^2+b_n^2}{2}})$ - can't recognize the pattern

Published on 17 Apr 2026 - 13:03

score 263 · Answer 6 · 2026-05-06 02:18:27

263

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Iterating a multiple of sine function makes a square wave

Published on 06 May 2026 - 2:18

score 368 · Answer 7 · 2026-04-15 23:37:36

368

Views

Prove using induction that $C(n) = C(n/5) + C(3n/4) + n$ is $O(n)$

Published on 15 Apr 2026 - 23:37

score 67 · Answer 8 · 2026-04-11 23:39:53

67

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How do I compute the generating function for this number sequence?

Published on 11 Apr 2026 - 23:39

score 355 · Answer 9 · 2026-03-26 22:13:05

355

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Simplifying this series of Laguerre polynomials

Published on 26 Mar 2026 - 22:13

score 230 · Answer 10 · 2026-03-26 12:53:33

230

Views

How do I prove the relationship between $I_n:=\int_{0}^{\pi}(\sin x)^ndx$ and $I_n=\frac{n-1}{n}I_{n-2}$ by partial Integration?

Published on 26 Mar 2026 - 12:53

score 117 · Answer 11 · 2026-04-16 01:53:21

117

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Does this family of sequences have the limit $\left(\frac{x^{2p}-y^{2p}}{2p(\ln x-\ln y)} \right)^{1/2p}$ for $p \in \mathbb{R}$?

Published on 16 Apr 2026 - 1:53

score 48 · Answer 12 · 2026-04-15 21:57:14

48

Views

Proof that linear difference operator, $(σ-1)^{k+1} (p) = 0$ for all $p$ $\epsilon$ $\mathbb{Q}[t]$, with $deg(p) \leq k$.

Published on 15 Apr 2026 - 21:57

score 373 · Answer 13 · 2026-04-12 09:09:38

373

Views

rearranging a linear first order recurrence

Published on 12 Apr 2026 - 9:09

score 119 · Answer 14 · 2026-04-11 09:32:38

119

Views

Finding a closed form for $\sum^{n}_{k=1} \frac{k}{(k+1)!} $

Published on 11 Apr 2026 - 9:32

score 91 · Answer 15 · 2026-04-12 12:49:38

91

Views

First-Order Linear Difference Equation with Constraint

Published on 12 Apr 2026 - 12:49

List Question

Prove an algorithm for logarithmic mean $\lim_{n \to \infty} a_n=\lim_{n \to \infty} b_n=\frac{a_0-b_0}{\ln a_0-\ln b_0}$

The sequence $(a_n)$ is given as $a_1=1, a_{2n} = a_n - 1, a_{2n+1} = a_n + 1$. $a_{2015}=$?

limiting point of a difference equation with coefficients related to a characteristic polynomial

Find the $m$ such $a_{n+1}=a^5_{n}+487$

Limit of the sequence $a_{n+1}=\frac{1}{2} (a_n+\sqrt{\frac{a_n^2+b_n^2}{2}})$ - can't recognize the pattern

Iterating a multiple of sine function makes a square wave

Prove using induction that $C(n) = C(n/5) + C(3n/4) + n$ is $O(n)$

How do I compute the generating function for this number sequence?

Simplifying this series of Laguerre polynomials

How do I prove the relationship between $I_n:=\int_{0}^{\pi}(\sin x)^ndx$ and $I_n=\frac{n-1}{n}I_{n-2}$ by partial Integration?

Does this family of sequences have the limit $\left(\frac{x^{2p}-y^{2p}}{2p(\ln x-\ln y)} \right)^{1/2p}$ for $p \in \mathbb{R}$?

Proof that linear difference operator, $(σ-1)^{k+1} (p) = 0$ for all $p$ $\epsilon$ $\mathbb{Q}[t]$, with $deg(p) \leq k$.

rearranging a linear first order recurrence

Finding a closed form for $\sum^{n}_{k=1} \frac{k}{(k+1)!} $

First-Order Linear Difference Equation with Constraint

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