# Tagged Questions

Questions regarding functions defined recursively, such as the Fibonacci sequence.

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### Solve the recurrence $a_n=3a_{n/3}+2$ given $a_0=1$ and $n$ is a power of $3$

Solve the recurrence $$a_n=3a_{n/3}+2$$ given $a_0=1$ and $n$ is a power of $3$ I am trying to study for my final using my previous quizzes, of which I got this question wrong. My instructor wants me ...
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### limit of $a_n$ when n to infinity. $a_1=\sqrt{k}$ and $a_n = \sqrt{k}^{a_{n-1}}$ . $0<k<1$.

I find a question on quora: limit of a sequence. Generalized Case 1 When you generalize this question like: \begin{align} a_1 &= \sqrt{k} \\ a_n &= \sqrt{k}^{a_{n-1}} \end{align} ...
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### Non-homogeneous Recurrence Relation with Fibonacci Sequence

I have this question in my assignment, I'm just not sure how to handle finding the closed form fully. I have most of it. Here's the question for context. Recall that the Fibonacci sequence is defined ...
I have a discrete evolution equation such that $$\rho(t+\tau) = M_0 \rho(t)M_0^\dagger+M_1 \rho(t)M_1^\dagger$$ $M_0\;\&\;M_1$ are two operators such that $tr(M_0^\dagger M_1)=0$ i.e. they are ...