List questions from recurrence-relations

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recurrence relation function definition

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$T(n) = nT(n-1) + 1$ with $T(1)=1$

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How to derive the following linear recurrence?

Published on 30 Mar 2018 - 13:56

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Measure of $A(\alpha):=\left\{ x \in \mathbb{R}^n: 0\le x_1\le x_2 \le...\le x_n \le \alpha \right\}$

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solving a recurrence function

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Homogeneous recurrence relation of degree 8 with one characteristic root

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Solve recurrence $T(n) = T(\frac34n) + \sqrt n$

Published on 25 Mar 2026 - 23:21

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Closed form of :$ (n+1)^4y_{n+1}-n^4y_{n}=2n+1$

Published on 25 Mar 2026 - 1:27

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If $\{a_n\}$ are the Fibonacci numbers, then does $\sum_{n=0}^{\infty} \frac{1}{a_n}$ converge?

Published on 30 Mar 2018 - 20:19

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exponential generating function - Fibonacci recurrence relation

Published on 25 Mar 2026 - 4:35

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Math Olympiad Question : $a_na_{n+1} = a_n^2 + 1, a_0 = 5$

Published on 25 Mar 2026 - 22:25

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How to get $2^p=(1+\sqrt{5})/2$ from the equation below?

Published on 31 Mar 2018 - 10:34

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How to prove a sequence is strictly increasing and bounded above?

Published on 26 Mar 2026 - 14:20

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Recurrence Relation derivatives of $x^x$

Published on 01 Apr 2018 - 20:55

List Question

Finding an explicit formula for $a_n$ defined recursively by $a_{n+1}=2a_n\frac{(n+2)}{n+1} $

recurrence relation function definition

$T(n) = nT(n-1) + 1$ with $T(1)=1$

How to derive the following linear recurrence?

Measure of $A(\alpha):=\left\{ x \in \mathbb{R}^n: 0\le x_1\le x_2 \le...\le x_n \le \alpha \right\}$

solving a recurrence function

Homogeneous recurrence relation of degree 8 with one characteristic root

Solve recurrence $T(n) = T(\frac34n) + \sqrt n$

Closed form of :$ (n+1)^4y_{n+1}-n^4y_{n}=2n+1$

If $\{a_n\}$ are the Fibonacci numbers, then does $\sum_{n=0}^{\infty} \frac{1}{a_n}$ converge?

exponential generating function - Fibonacci recurrence relation

Math Olympiad Question : $a_na_{n+1} = a_n^2 + 1, a_0 = 5$

How to get $2^p=(1+\sqrt{5})/2$ from the equation below?

How to prove a sequence is strictly increasing and bounded above?

Recurrence Relation derivatives of $x^x$

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