This series was put forward by Fibonacci in Italy in the13rd century, so it is called Fibonacci series. This order is determined by the following recursive relation:

F0=0，F 1= 1

Fn+2 = Fn+Fn+ 1(n & gt； =0)

Its general formula is

Fn= 1/ n power of root number 5 {[( 1+ root number 5)/2]-n power [( 1- root number 5)/2] }(n is a positive integer).

Fibonacci sequence has many magical properties.

The asymptotic value of Fn/Fn+ 1 in Fibonacci sequence is (√5- 1)/2 (golden section, ≈0.6 18).

The asymptotic value of Fn+ 1/Fn is (√ 5+1)/2 ≈1.618.

The landlord misunderstood, this is the limit ratio, that is to say, the greater the number of terms n, the closer it is to this result, and Fibonacci series itself is not a geometric series! Its essence is difference equation. Please refer to relevant materials for specific solutions.

When two M's are divisible by n, Fm is divisible by Fn.

Let A and B be natural numbers, and the relationship between them is recursive.

F0=0，F 1= 1

fn+2 = aFn+ 1+bFn(n & gt； =0)

The general formula for generating a sequence is

The n power of Fn = 1/√L {[(a+√L)/2]- n power [(1-√ l)/2] (l = a 2+4b, n > = 1) and has the property that when m can be integer by n.