Chapter 18.2, Problem 60PS

To determine

To conclude:

Assuming that young pair of rabbits become adults after two months and produce an offspring. This process continues and a “Colony” of rabbits is produced at the end of $n$ months. The growth rate sequence of the colony is defined and it is assumed that the rate is convergent. The recursion formula is used in the below equation,

$\frac{a_{n+1}}{a_n}=1+\frac{a_{n-1}}{a_n}$

and let $L=\underset{n\to \infty }{\lim }{r}_n$

Finally, the conclusion has to be made to check whether L satisfies this equation $L=1+\frac{1}{L}$.