This series begins with the third item, each item is equal to the sum of the first two items. Interestingly, such a series of completely natural numbers are actually represented by irrational numbers.

With the increase of the number of series items, the ratio of the former item to the latter item is getting closer and closer to the golden section value of 0.6 180339887.

Starting from the second term, the square of each odd term is more than the product of the first two terms 1, and the square of each even term is less than the product of the first two terms 1. (Note: Odd and even terms refer to the parity of terms, not the parity of numbers in exponential columns. For example, the square of the fifth term is more than the product of the first two terms 1, and the square of the fourth term is less than the product of the first two terms 1. )

The nth term of Fibonacci sequence also means that the set {1, 2, ..., n} does not contain adjacent positive integers.

Other properties of Fibonacci sequence (f(n), f(0)=0, f( 1)= 1, f(2)= 1, f (3) = 2 ...);

1 . f(0)+f( 1)+f(2)+…+f(n)= f(n+2)- 1

2 . f( 1)+f(3)+f(5)+…+f(2n- 1)= f(2n)

3.f(2)+f(4)+f(6)+…+f(2n)？ =f(2n+ 1)- 1

4.[f(0)]^2+[f( 1)]^2+…+[f(n)]^2=f(n]f(n+ 1)

5.f(0)-f( 1)+f(2)-…+(- 1)^n f(n)=(- 1)^n[f(n+ 1)-f(n)]+ 1

6 . f(m+n)= f(m- 1)f(n- 1)+f(m)f(n)

Using this, we can compile a program with a time complexity of only O(log? N) program.

7.[f(n)]^2=(- 1)^(n- 1)+f(n- 1]f(n+ 1)

8.f(2n- 1)=[f(n)]^2-[f(n-2)]^2

9.3f(n)=f(n+2)+f(n-2)

10 . f(2n-2m-2)[f(2n)+f(2n+2)]= f(2m+2)+f(4n-2m)？ [? N > m ≥- 1, and n≥ 1] Fibonacci sequence