- #1
math_grl
- 49
- 0
Ok I need to know which is the right answer for evaluating the continued fraction [tex]\langle 1, 2, 1, 2, \ldots \rangle[/tex]?
Here's my work:
[tex]x = 1 + \frac{1}{2+x} \Rightarrow x^2 + x - 3 = 0[/tex] and by quadratic formula, we get [tex]x = \frac{-1 \pm \sqrt{13}}{2}[/tex] but we only want the positive root so I get [tex]x = \frac{-1 + \sqrt{13}}{2}[/tex] for my answer but the answer given was [tex]x = \frac{1 + \sqrt{3}}{2}[/tex], so I'm confused at which it is...
Moreover, I can't seem to find any other example except for [tex]\langle 1, 1, 1, \ldots \rangle[/tex] to see if I'm doing my computation right. Please help.
Here's my work:
[tex]x = 1 + \frac{1}{2+x} \Rightarrow x^2 + x - 3 = 0[/tex] and by quadratic formula, we get [tex]x = \frac{-1 \pm \sqrt{13}}{2}[/tex] but we only want the positive root so I get [tex]x = \frac{-1 + \sqrt{13}}{2}[/tex] for my answer but the answer given was [tex]x = \frac{1 + \sqrt{3}}{2}[/tex], so I'm confused at which it is...
Moreover, I can't seem to find any other example except for [tex]\langle 1, 1, 1, \ldots \rangle[/tex] to see if I'm doing my computation right. Please help.