Solution: (a) Fibonacci posed the following problem: Suppose that rabbits live forever

Chapter 11, Problem 83

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(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 month? Show that the answer is , where is the Fibonacci sequence defined in Example 3(c). (b) Let and show that . Assuming that is convergent, find its limit.

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