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How do I show convergence of continued fraction?

Lets take the sequence $x_n=3+\frac{3}{x_{n-1}}$ and $x_1=3$ In case of convergence the limit of the sequence will verifie the following equation $$L=3+\frac{3}{L}\implies L^2=3L+3\iff L=\frac{3\pm\...
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What are the applications of continued fractions?

This article by Carlo Sanna, based on lectures by Michel Waldschmidt in the Proceedings of the Roman Number Theory Association contains common applications of continued fractions, some of which can be ...
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Are there continued fraction expressions for $e^{p/q}$?

Here I provide some more information; Robert Israel answered to my finding in my above comment in the sci.math-newsgroup. I don't have a link, so I paste the msg from my downloaded copy from then: <...
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