+934 Call this "x" : \(\cfrac{9}{9 + \cfrac{9}{9 + \cfrac{9}{9 + \dotsb}}} \)
Which simplifies to: \(\frac{9}{9+x}\)
From this, we can set up the equations:
\(x=\frac{9}{9+x}\)
\(x^2+9x=9\)
\(x^2+9x-9=0\)---> This quadratic equation had 2 solutions, one positive and one negative, for obvious reasons we can rule out the negative solution. This means that the positive solution is our answer:
\(x=\frac{-9+3\sqrt{13}}{2}\)
I appreciate your time!
*Note: I'm not 100% sure about my answer. If anyone sees anything wrong with my thinking process, make sure to point it out!
