Problem:
If $x = \frac{418}{411}$, then find $\frac{1}{x+\frac{1}{x+\frac{1}{x+\ddots}}}$.
Answer:
$\frac{1}{411} \left(13 \sqrt{1258}-209\right)$
{'source': 'AMPS', 'file': 'amps/mathematica/number_theory/continued_fraction/17011.txt'}