Ratio of Consecutive Fibonacci Numbers/Proof 2

Proof
From Continued Fraction Expansion of Golden Mean: Successive Convergents, the $n$th convergent of the continued fraction expansion of $\phi$ is given as:
 * $C_n = \dfrac {f_{n + 1} } {f_n}$

The result follows as a result of Value of Simple Infinite Continued Fraction.