List questions from recurrence-relations

Published on 13 Mar 2019 - 17:06

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Non linear recurrence

Published on 13 Mar 2019 - 19:09

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Prove that $a_{n+1}=\frac{a_n^2+4}{a_{n-1}}$ recursion formula is equivalent to $\frac{a_{n+1}+a_{n-1}}{a_n}=6$ if $a_1=1, a_2=5$ $\forall n \gt1$

Published on 14 Mar 2019 - 13:31

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How to solve $y_{n}=\frac{4}{n(n-1)} y_{n-2}$

Published on 14 Mar 2019 - 16:02

163

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Solve the recurrence $b_1 = 2$ for $b_n = 3b_{n-1} + 5$

Published on 26 Mar 2026 - 12:41

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Help Solving Recurrence Relation: $a_n = n^3a_{n-1} + (n!)^3$

Published on 28 Mar 2026 - 10:03

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Does $(n+1)(n-2)x_{n+1}=n(n^2-n-1)x_n-(n-1)^3x_{n-1}$ with $x_2=x_3=1$ define a sequence that is integral at prime indices?

Published on 26 Mar 2026 - 1:11

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Prove recurrence relation by induction

Published on 31 Mar 2026 - 10:04

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The $n$th derivative of $f(e^x)$

Published on 15 Mar 2019 - 15:47

67

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Solve $a_{n+2}=a_{n} \times \frac{(n+1)(n+4)}{(n+2)(n+3)}$

Published on 15 Mar 2019 - 19:58

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is it possible to find a closed expression to this?

Published on 31 Mar 2026 - 10:07

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Find the solution to the recurrence relation $a_{n} = 3a_{n−1} +4a_{n−2}$ with initial terms $a_{0}=5$ and $a_{1} =8$

Published on 16 Mar 2019 - 13:34

68

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How to solve this harmonic progression ? summation $\sum _{i=1} ^{\log(n)-1} \frac 1 {\log(n)-i}$?

Published on 29 Mar 2026 - 9:11

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Does this recursive function have a function in terms of n?

Published on 25 Mar 2026 - 21:44

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Solving the recurence $T(n) = T(n/5) + T(7n/10) + n$ using substitution method

Published on 27 Mar 2026 - 1:46

List Question

slightly different from AGM

Non linear recurrence

Prove that $a_{n+1}=\frac{a_n^2+4}{a_{n-1}}$ recursion formula is equivalent to $\frac{a_{n+1}+a_{n-1}}{a_n}=6$ if $a_1=1, a_2=5$ $\forall n \gt1$

How to solve $y_{n}=\frac{4}{n(n-1)} y_{n-2}$

Solve the recurrence $b_1 = 2$ for $b_n = 3b_{n-1} + 5$

Help Solving Recurrence Relation: $a_n = n^3a_{n-1} + (n!)^3$

Does $(n+1)(n-2)x_{n+1}=n(n^2-n-1)x_n-(n-1)^3x_{n-1}$ with $x_2=x_3=1$ define a sequence that is integral at prime indices?

Prove recurrence relation by induction

The $n$th derivative of $f(e^x)$

Solve $a_{n+2}=a_{n} \times \frac{(n+1)(n+4)}{(n+2)(n+3)}$

is it possible to find a closed expression to this?

Find the solution to the recurrence relation $a_{n} = 3a_{n−1} +4a_{n−2}$ with initial terms $a_{0}=5$ and $a_{1} =8$

How to solve this harmonic progression ? summation $\sum _{i=1} ^{\log(n)-1} \frac 1 {\log(n)-i}$?

Does this recursive function have a function in terms of n?

Solving the recurence $T(n) = T(n/5) + T(7n/10) + n$ using substitution method

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