Fibonacci posed the following problem: Suppose that rabbits live forever and that every month each pair produces a new pair which becomes productive at age 2 months. If we start with one newborn pair, how many pairs of rabbits will we have in thenth month? Show that the answer isf_n, where{f_n}is the Fibonacci sequence defined in thisexample.

Leta_n=f_{n+ 1}/f_n and show thata_n1= 1 + 1/a_n2.

Assuming that{a_n}is convergent, find its limit. (If an answer does not exist, enter DNE.)