List questions from recurrence-relations

267

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Find $\lim\limits_{n\to\infty}\frac{a_1+a_2+...+a_n}{1+\frac{1}{\sqrt2}+...+\frac{1}{\sqrt{n}}}$ with $a_1=1$ and $a_{n+1}=\frac{1+a_n}{\sqrt{n+1}}$

Published on 09 Mar 2019 - 18:57

58

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How to solve the recurrence relation $G(k) = 2^{(1.5)\cdot 2^k}G(k-1) + \left(2 ^{3 \cdot (2^k)}\right)\left(2 ^{ (2k)}\right) \cdot k$

Published on 10 Mar 2019 - 10:14

153

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Proof of patterns in Fibonacci words

Published on 26 Mar 2026 - 10:59

607

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Palindrome Fibonacci words

Published on 25 Mar 2026 - 4:38

184

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Generalized geometric series with long range dependence

Published on 10 Mar 2019 - 22:28

132

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Recurrence relation over a finite alphabet

Published on 11 Mar 2019 - 4:06

77

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Solving a differential equation using the Frobenius method

Published on 22 Feb 2026 - 23:23

98

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Combinatorial formula for linear recurrence relations

Published on 11 Mar 2019 - 19:00

38

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Solving the Utopian Tree recurrence

Published on 28 Mar 2026 - 10:03

630

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Solving a recurrence using the Master Theorem

Published on 25 Mar 2026 - 21:53

256

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Using the Master Theorem to solve a recurrence

Published on 25 Mar 2026 - 21:45

217

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When does the recurrence $a_k = 3a_{k - 1} + 1$ reach a power of 2?

Published on 25 Mar 2026 - 6:05

115

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Limit of a function, given the recurrence relation

Published on 30 Mar 2026 - 21:07

209

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Concrete Mathematics

Published on 12 Mar 2019 - 15:09

48

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strange recurrence relation and limit

Published on 12 Mar 2019 - 17:36

List Question

Find $\lim\limits_{n\to\infty}\frac{a_1+a_2+...+a_n}{1+\frac{1}{\sqrt2}+...+\frac{1}{\sqrt{n}}}$ with $a_1=1$ and $a_{n+1}=\frac{1+a_n}{\sqrt{n+1}}$

How to solve the recurrence relation $G(k) = 2^{(1.5)\cdot 2^k}G(k-1) + \left(2 ^{3 \cdot (2^k)}\right)\left(2 ^{ (2k)}\right) \cdot k$

Proof of patterns in Fibonacci words

Palindrome Fibonacci words

Generalized geometric series with long range dependence

Recurrence relation over a finite alphabet

Solving a differential equation using the Frobenius method

Combinatorial formula for linear recurrence relations

Solving the Utopian Tree recurrence

Solving a recurrence using the Master Theorem

Using the Master Theorem to solve a recurrence

When does the recurrence $a_k = 3a_{k - 1} + 1$ reach a power of 2?

Limit of a function, given the recurrence relation

Concrete Mathematics

strange recurrence relation and limit

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