Fibonacci Series | Fibonacci Sequence in Python

Fibonacci sequence is a set of numbers that start with 1 or 0 followed by a 1 proceeds on the rule that each number.

Fibonacci number is equal to the sum of the preceding two numbers.

F(n) = 0, 1, 1, 2, 3, 5, 8, 13....

In mathematical terms, the sequence F(n) of Fibonacci number is defined by the recurrence relation.

F(n) = F(n-1) + F(n-2)

Where seed values are : 

F(0) = 0 and F(1) = 1

Method: 1 - Using For Loop

For printing the sequence of Fibonacci sequence with the help of for loop.

1. Take the input of values, want to generate the Fibonacci sequence.
2. Initilized a = 0 and b = 0
3. if n < = 0 , then print the Message for used "Please Enter the Positive Integer Number" otherwise go to step 4
4. if n == 1, it will print the 1 terms of the Fibonacci Series. otherwise go to step 5
5. Print the two Starting two terms of the fiboanacci Series and after that Start a for loop while range is n -2 then print the sequence of the Fibonacci Series. 
6. print(c, end =" "), here c = a + b
7. update the values , a = b, b = c and so, up to the required term. 

n = int(input("How many Terms the users wants to print : "))

a = 0
b = 1

if n<=0:
    print("Please Enter the Positive Integer Number")
    
else:
    if n == 1:
        print("Fibonacci Sequence of the Number up to ", n)
        print(a, end=" ")
    else:
        print("Sequence ( Series ) of Fibonacci : ")
        print(a , b, end = " ")
        for i in range(n-2):
            c = a + b
            print(c, end = " ")
            a = b
            b = c

Method:2 - Using While loop

1. Take input the number of values to generate the Fibonacci Series.
2. Initialize the count = 0, a = 0, and b = 1
3. if the n < = 0
4. print"Error Message" as it is not a valid number for Gibonacci Series.
5. if n = 1, it will print a value
6. while count < n
7. print(a)
8. c = a + b
9. update the variable a = b, b = c and so no, upto the required term.

n = int(input("How many Terms the users wants to print : "))

count = 0
a = 0
b = 1

if n<=0:
    print("Please Enter the Positive Integer Number")
    
elif n == 1:
    print("Fibonacci Sequence of the Number up to ", n)
    print(a, end=" ")
else:
    print("Sequence ( Series ) of Fibonacci : ")
    while count < n:
        print(a, end = " ")
        c = a + b
        a = b
        b = c
        count += 1

Method: 3 - Using Recursion

def Fibonacci(n):
    if n < 0:
        print("Enter the Positive Integer Number")
    elif n == 0:
        return 0
    elif n == 1 :
        return 0
    elif n == 2 or n == 3:
        return 1
    else:
        return Fibonacci(n-1) + Fibonacci(n-2)
    
        

n = int(input("How many Terms the users wants to print : "))

print(Fibonacci(n))

Thanks...

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