Ratio of Consecutive Lucas Numbers

Theorem
For $n \in \N$, let $L_n$ be the $n$th Lucas number.

Then:
 * $\displaystyle \lim_{n \mathop \to \infty} \frac {L_{n + 1} } {L_n} = \phi$

where $\phi = \dfrac {1 + \sqrt 5} 2$ is the golden mean.