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:
 * $C_n = \dfrac {f_{n + 1} } {f_n}$

The result follows from Continued Fraction Expansion of Irrational Number Converges to Number Itself.