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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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