Feb 28, 2020 · Yet another example from this question is this recursive sequence: which has the following closed form formula: So, my question is, how does one come up with these …

Finding a closed-form formula for a sequence that is defined recursively Ask Question Asked 11 years ago Modified 5 years, 10 months ago

Jan 8, 2024 · 0 I am working on a recursive sequence and wondering if it's possible to convert it into a non-recursive form. The sequence is defined as follows: an = an−1 ×(n+1)+ n! a n = a n …

Explore related questions sequences-and-series recursive-algorithms closed-form See similar questions with these tags.

Nov 11, 2017 · Unfortunately I am quite confused here because of the recursive definition. Question: How can I show show that the sequences converges and how can I find a limit value?

Apr 16, 2017 · The generation of such a sequence is a requirement in the definition. Here is an example of a recurrence relation: $$ a_1 = 1$$ $$ a_n = na_ {n-1}$$ So in short. Recurrent is …

Nov 29, 2024 · I'm pretty sure that means that if the sequence does converge, it must converge to $1$, but "I'm pretty sure" isn't much of a proof. I don't see any way to find an explicit form for …

Apr 9, 2019 · Search about linear homogeneous recursive sequences, there's a pretty easy algorithm, you just need to analyze some specific polynomial

Hence, by strong induction, the result holds for all natural numbers. Is this the correct way to prove a formula for a recursive sequence using strong induction?

Something that should be mentioned is that even though we can find a closed form for the fibonacci sequence, the best way to calculate a term in the sequence is by using the recursion.