In Problems 58-60, further assume that young rabbits become adults after two months and produce another pair of offspring at that time. A rabbit breeder begins with one adult pair. Let \(a_{n}\) denote the number of adult pairs of rabbits in this "colony" at the end of \(n\) months.

Assume that the growth rate sequence \(\left\{r_{n}ight\}\) defined in Problem 59 converges, and let \(L=\lim _{n ightarrow \infty} r_{n}\). Use the recursion formula in Problem 58 to show that \[\frac{a_{n+1}}{a_{n}}=1+\frac{a_{n-1}}{a_{n}}\]
and conclude that \(L\) must satisfy the equation \[L=1+\frac{1}{L}\]
Use this information to compute \(L\).