# Coding challenge

The "golden ratio" is worth reading about on Wikipedia. As a number, it is $\rho=\frac{1}{2}(1+\sqrt{5})$, where $\rho$ is the golden ratio. Write code to show that
1. $\rho=\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+...}}}}$
2. $\rho^n=\rho^{n-1}+\rho^{n-2}$
3. $\rho=\rho^{-1}+\rho^{-2}+\rho^{-3}+...$
(From Cheney, p. 669.)