Fibonacci Sequence--the breeding problem of rabbits

The Fibonacci sequence is also known as the "rabbit sequence" because of the example of the breeding of the rabbit by the mathematician Leonardo's Fibonacci. Fibonacci sequence in general, rabbits are fertile after two months of birth, and a pair of rabbits can produce a pair of rabbits each month. If all the rabbits are not dead, how many pairs of rabbits can be bred in a year?

We may as well take the new born pair of rabbits to analyze:

The first month the rabbit has no reproductive ability, so it is a pair;

Two months later, the birth of a pair of small rabbits a total of two pairs;

Three months later, the old rabbit gave birth to another pair, because the rabbit has no reproductive capacity, so altogether is three pairs;

---to list the following table: months: 0,1,2,3,4,5,6,7,8,9,10,11,12

Rabbit logarithm: 1,1,2,3,5,8,13,21,34,55,89,144,233

The digital 1,1,2,3,5,8---in the table Form a series. This series is concerned with the very obvious characteristics, that is: the sum of the preceding two adjacent, constitute the latter. This series is the Italian medieval mathematician Fibonacci in the Abacus book, the general formula of this series, in addition to having a (n+2) =an+a (n+1)/The nature, can also prove that the general formula is: an=1/√[(1+√5/2) n (1-√5/2) n] (n= ...)

Fibonacci Sequence--the breeding problem of rabbits