#1**0 **

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!

HELPMEEEEEEEEEEEEE May 25, 2020