Evaluate: $$S=1+ \frac{1}{2+ \dfrac{1}{4+ \dfrac{1}{8+ \dfrac{1}{16 +\cdots} }} }$$
What have I done, so far?
Nothing, couldn't think of a way to solve it. But I know it is around 1.46.
I want to solve it myself, so hint on how to solve will be sufficent.