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**hempy**- Replies: 2

Start with 2 baby rabbits, 1 male and 1 female. These baby rabbits became adult rabbits the next month. The month after that they produce a pair (one male, one female) of baby rabbits. Now in each subsequent month, each pair of baby rabbits reaches adulthood and each pair of adult rabbits produces a new pair(one male, one female) of baby rabbits.

Hence, the Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 21,...

Question: How many pairs of rabbits will there be after n months?

Explain why the answer is F(subn).

Any help would be much appreciated.

**hempy**- Replies: 8

Let a(sub0) and r be fixed real numbers with r ≠ 0 and r ≠ 1, and suppose that for each n ∈ N, a(subn) = r*a(subn-1).

For every nonnegative integer n, a(subn) = a(sub0) * r^n.

Prove by induction.

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