Part 2/6:
In the classic rabbit problem, one begins with a single pair of rabbits. Each pair of rabbits matures after two months, and every month thereafter, each mature rabbit pair produces a new pair that also lives indefinitely. The problem can be stated as follows: how many pairs of rabbits are present in the nth month?
Deriving the Fibonacci Sequence
To form a solution, we denote ( a_n ) as the number of rabbit pairs in the nth month. The evolution of the rabbit pairs can be deciphered with the following observations:
Month 1 ( ( a_1 ) ): There is only one pair of rabbits.
Month 2 ( ( a_2 ) ): The first pair hasn't yet produced offspring. Still only one pair exists, so ( a_2 = 1 ).