Evaluating Continued Fraction: \langle 1, 2, 1, 2, \ldots \rangle

[math_grl]

Ok I need to know which is the right answer for evaluating the continued fraction \langle 1, 2, 1, 2, \ldots \rangle?

Here's my work:
x = 1 + \frac{1}{2+x} \Rightarrow x^2 + x - 3 = 0 and by quadratic formula, we get x = \frac{-1 \pm \sqrt{13}}{2} but we only want the positive root so I get x = \frac{-1 + \sqrt{13}}{2} for my answer but the answer given was x = \frac{1 + \sqrt{3}}{2}, so I'm confused at which it is...

Moreover, I can't seem to find any other example except for \langle 1, 1, 1, \ldots \rangle to see if I'm doing my computation right. Please help.

 

[Petek]

Your equation for x is incorrect. It should be

1 + \frac{1}{2 + \frac{1}{x}}

 

[math_grl]

that's embarassing.

 

[Petek]

You'll do better next time!