In 1202, the Italian mathematician Fibonacci put forward a difficult problem: in the first month, he bought a pair of rabbits, in the second month, the rabbits grew into big rabbits, and in the third month, he gave birth to a pair of rabbits. A big rabbit can give birth to a pair of rabbits every month. What is the logarithm of rabbits in a family that buys rabbits and raises rabbits?

1, 1,2,3,5,8, 13,2 1,.

Whoever writes more is smart. This intellectual game was very popular at that time. This series is called Fibonacci series. Later Fibonacci gave the recurrence formula of this sequence:

a 1= 1，a2= 1，a(m+2)=a(m+ 1)+am，(m≥ 1，m∈Z)

Later, people tried to find the general formula of the sequence, but for a long time failed. It was not until more than two hundred years later that the French mathematician Binet.Alfred finally came up with the general formula:

an={[(√5+ 1)^n]/2-[( 1-√5)^n]/2]}÷√5

Surprisingly, the general term of a series containing positive integers is a complex fraction containing irrational numbers!

The derivation of this general term is very complicated and cannot be described here.

Fibonacci sequence is wonderful, the former term is numerator and the latter term is denominator:

2/3,3/5,5/8.8/ 13,. is the fractional representation of the golden section number 0.6 18.

Fibonacci sequence is as widely used as the golden section. It is widely used in scientific research, literature, art, sports, medicine and many other aspects. For more than a thousand years, the research on it has been carried out enthusiastically and gradually developed. There are many related papers and monographs. If you are interested, you can go to the bookstore to buy some popular brochures.