(a) 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 the nth month? Show that the answer is fn, where {fn} is the Fibonacci sequence defined in Example 3(c).
(b) Let an = fn+ 1 / fn and show that an–1 = 1 + 1/an–2. Assuming {an} that is convergent, find its limit.