How to Write Python Fibonacci Series program using While Loop, For Loop, and Recursion?. As per Mathematics, Python Fibonacci Series or Fibonacci Numbers in Python are the numbers that are displayed in following sequence. Fibonacci Series = 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 …

If you observe the above pattern, First Value is 0, Second Value is 1 and the subsequent number is the result of sum of the previous two numbers. For example, Third value is (0 + 1), Fourth value is (1 + 1) so on and so forth.

## Python Fibonacci Series program Using While Loop

This Python program allows the user to enter any positive integer. Next, this program display the Python fibonacci series of number from 0 to user specified number using Python While Loop

# Python Fibonacci series Program using While Loop # Fibonacci series will start at 0 and travel upto below number Number = int(input("\nPlease Enter the Range Number: ")) # Initializing First and Second Values of a Series i = 0 First_Value = 0 Second_Value = 1 # Find & Displaying Fibonacci series while(i < Number): if(i <= 1): Next = i else: Next = First_Value + Second_Value First_Value = Second_Value Second_Value = Next print(Next) i = i + 1

**OUTPUT**

**ANALYSIS**

This python fibonacci series program allows the user to enter any positive integer and then, that number is assigned to variable Number. Next, We declared three integer variables i, First_Value and Second_Value and assigned values as we shown above.

The below While loop make sure that the loop starts from 0 and it is less than the user given number. Within the While loop of fibonacci series in python program, we used If statement.

- If i value is less than or equal to 1, then Next = i
- If i value is greater than 1, perform calculations inside the Else block.

while(i < Number): if(i <= 1): Next = i else: Next = First_Value + Second_Value First_Value = Second_Value Second_Value = Next print(Next) i = i + 1

Let us see the working principle of this while loop in this Python Fibonacci Series example in the iteration wise.

In this python fibonacci series example, User Entered value: Number = 4 and i = 0, First_Value = 0, Second_Value = 1

**First Iteration**

- While (0 < 4) is TRUE so, program start executing statements inside the while loop
- Within the while loop we have If statement and the condition if (0 <= 1) is TRUE. So, Next = 0 and compiler exit from if statement block
- Print statement
**print(Next)**print the value 0 - Lastly, i incremented to 1

**Second Iteration**

- While (1 < 4) is TRUE. So, Python Fibonacci Series program start executing statements inside the while loop
- Within the while loop we have If statement and the condition if (1 <= 1) is TRUE. So, Next = 1 and compiler exit from if statement block
- Print statement
**print(Next)**print the value 1 - i incremented to 1

**Third Iteration**

While (2 < 4) is TRUE in this fibonacci series in python. Within the while loop, we have If statement and the condition if (2 <= 1) is FALSE so statements inside the else block start executing

Next = First_Value + Second_Value

Next = 0 + 1 = 1

First_Value = Second_Value = 1

Second_Value = Next = 1

Next, Print statement **print(Next)** print the value 1. Lastly, i incremented to 1

**Fourth Iteration**

While (3 < 4) is TRUE. So, program start executing statements inside the while loop. Within the while loop we have If statement and the condition if (3 <= 1) is FALSE so statements inside the else block start executing

Next = First_Value + Second_Value

Next = 1 + 1 = 2

First_Value = Second_Value = 1

Second_Value = Next = 2

Next, Print statement **print(Next)** print the value 2. Lastly, i incremented to 1

**Fifth Iteration**

While (4 < 4) is FALSE so, program exit from the while loop.

From the above, Our final output of Next values are: 0 1 1 2

## Fibonacci Series program Using For Loop

This Python Fibonacci Series using for loop example allows the user to enter any positive integer. Next, this program display the fibonacci series of number from 0 to user specified number using Python For Loop

# Python Fibonacci series Program using For Loop # Fibonacci series will start at 0 and travel upto below number Number = int(input("\nPlease Enter the Range Number: ")) # Initializing First and Second Values of a Series First_Value = 0 Second_Value = 1 # Find & Displaying Fibonacci series for Num in range(0, Number): if(Num <= 1): Next = Num else: Next = First_Value + Second_Value First_Value = Second_Value Second_Value = Next print(Next)

**OUTPUT**

We just replaced the While loop in the above fibonacci series example with the For loop. If you don’t understand the for loop then please refer For Loop article here: Python For Loop

## Python Fibonacci Series program Using Recursion

This Fibonacci Series program allows the user to enter any positive integer, and then this program display the fibonacci series of number from 0 to user specified number using Recursion concept.

# Python Fibonacci series Program using Recursion # Recursive Function Beginning def Fibonacci_series(Number): if(Number == 0): return 0 elif(Number == 1): return 1 else: return (Fibonacci_series(Number - 2)+ Fibonacci_series(Number - 1)) # End of the Function # Fibonacci series will start at 0 and travel upto below number Number = int(input("\nPlease Enter the Range Number: ")) # Find & Displaying Fibonacci series for Num in range(0, Number): print(Fibonacci_series(Num))

**OUTPUT**

**ANALYSIS**

In this Python Fibonacci Series program example we defined a function. Following function accept integer values as parameter value and return value

def Fibonacci_series(Number):

Lets see the ElIf statement inside the above specified functions

- if (Number == 0) check whether the given number is 0 or not. If it is TRUE, function return the value Zero.
- if (Number == 1) check whether the given number is 1 or not. If it is TRUE, function return the value One.
- and, if the number is greater than 1 then the statements inside the else block executed.

Within the Else block of this python fibonacci series we called the function recursively to display the Fibonacci series.

return (Fibonacci_series(Number - 2)+ Fibonacci_series(Number - 1))

For the demonstration of fibonacci series, Number = 2

(Fibonacci_series(Number – 2)+ Fibonacci_series(Number – 1))

(Fibonacci_series(2 – 2)+ Fibonacci_series(2 – 1))

It means, (Fibonacci_series(0)+ Fibonacci_series(1))

return (0 + 1) = return 1

**NOTE:** For Recursive functions it is very important to place a condition before using the function recursively. Otherwise, we end up in infinite execution (Same like infinite Loop).

Please be careful :)