Fibonacci series in python

Fibonacci Series

Fibonacci series is 0,1,1,2,3,5,8,13,21,34,............,infinity.

It is a sequence of number which follow some type of algorithm

the alogrithm is 

let 

i = index position 

a = it is a array of number 

so to find a[i+1] = a[i]+a[i-1].

Note : fibonacci series always start with 0 and 1 and goes upto infinity.you can't start with your own values.

Explanation:

1. 0 and 1 in starting is default values 

2. if we go further the algorithm start adding previous 2 value and the answer is the next value.

    as you can see the previous two value is 0 and 1 after adding both we get 1 as our 3rd value.

    after that adding 1 and 1 we get our 4th value as 2 this entire cycle goes like this only.

i think you get better understanding about fibonacci series we move further on coding of fibo 

in python:

Flowchart:

coding:

without recursion function:

def fibonacci(n):

    a = 0

    b = 1

    if n <= 0:

        print("Incorrect input")

    else:

        print(a,"\n",b)


        for i in range(2,n):

            c = a + b

            print(c)


            a = b

            b = c

        return b

 

fibonacci(9)




output:

0

1

1

2

3

5

8

13

21

Explanation :

in the code we pass 9 as a last index number of Fibonacci it mean we just

won't 9 numbers only that.

as condition that 0 and 1 is the default starting two value we pass to A and B.

after that we check conditions

1.check weather the value pass by user is less that 0(-ve) than return

incorrect input.

2.in else part we start our loop we first print A and B value then the loop

  is started with the range from 2,....,N.

  in loop we do C=A+B because in Starting 2 value is A=0 and B=1 .

we simply add A and B and store it in C variable.

after that we print C and then we swap the value A=B and B=C .

this is until for loop condition gets false.

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