Problem:
If $x = \frac{137}{508}$, then find $\frac{1}{x+\frac{1}{x+\frac{1}{x+\ddots}}}$.
Answer:
$\frac{5 \sqrt{42041}-137}{1016}$
{'source': 'AMPS', 'file': 'amps/mathematica/number_theory/continued_fraction/4724.txt'}