golden ratio of a fraction
This is a computational exercise, but I am looking to attempt on a calculation on a golden ratio. I am trying to compute that of the continued fraction for the golden ratio $(1+\sqrt{5})/2$, and I am starting from the definition of $(a+b)/a = a/b$.
Simple, you have $$\frac{a+b}{b}=\frac{b}{a}$$ and $$\frac{a+b}{b}=1+\frac{a}{b}=1+\frac{1}{\frac{b}{a}}=1+\frac{1}{\frac{a+b}{b}}$$ and the process continues onward.