Questions tagged [continued-fractions]

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2
votes
3answers
423 views

Truncate an infinite continued fraction at order 2000

I want to solve an equation which contains an infinite continued fraction $F(n)$. Then I must (obviously) truncate this continued fraction at $n=2000$. The problem here is that Mathematica does not ...
7
votes
5answers
731 views

How can I write Mathematica code for this continued fraction with alternating terms?

$$\varphi+\cfrac{1}{\varphi^{-1}+\cfrac{1}{\varphi+\cfrac{1}{\varphi^{-1}+\cfrac{1}{\varphi+\cdots}}}}$$ I saw this continued fraction on Facebook. I need the Mathematica code for this using ...
5
votes
1answer
1k views

Negative Continued Fraction of a Rational

The $n^{\text{th}}$ negative continued fraction convergent $x_n$ of a positive real $x$ is computed by the nested function \begin{align} x_n = k_1 - \frac{1}{k_2 - \frac{1}{k_3 - \dots - \tfrac{1}{k_n}...