1. ## infinite continued fraction

Hi, I mostly know how to do a question like this if it was finite, but since it is infinite I need some help.

q: express the continued fraction expansion [1,5,1,5,1,5,...] in the form

$\frac{a+b \sqrt{c}}{d}$ where a,b,c and d are integers.

Thanks for any help.

2. ## Re: infinite continued fraction

Let
$x= 1+\frac{5}{1+ \frac{5}{1+ \cdot\cdot\cdot}}$
From which it follows that $x= 1+ 5/x$.