2. In 1228 Leonardo of Pisa, known as Fibonacci, posed the following problem in his Liber Abaci:
A certain man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair which from the second month on becomes productive?
Suppose rabbits never die. Let fn be the number of pairs of rabbits after n months.
a. How is fn+2 related to fn+1 and fn? Why? [3]
b. Find the answer to Leonardo's question. [2]
Department of Mathematics
Trent University