## Fibonacci Series in Python

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.

In this article we will show you, How to Write Python Fibonacci Series program using While Loop, For Loop and Recursion.

## Python Fibonacci Series program Using While Loop

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

**PYTHON CODE**

# 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.

Below While loop will make sure that, the loop will start 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 will be 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 program in the iteration wise.

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

**First Iteration**

- While (0 < 4) is TRUE so, program will 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 will exit from if statement block
- Print statement
**print(Next)**will print the value 0 - Lastly, i will be incremented to 1

**Second Iteration**

- While (1 < 4) is TRUE so, Python Fibonacci Series program will 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 will exit from if statement block
- Print statement
**print(Next)**will print the value 1 - Lastly, i will be 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 will 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)** will print the value 1. Lastly, i will be incremented to 1

**Fourth Iteration**

While (3 < 4) is TRUE so, program will 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 will 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)** will print the value 2. Lastly, i will be incremented to 1

**Fifth Iteration**

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

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

## Python Fibonacci Series program Using For Loop

This Python Fibonacci Series program allows the user to enter any positive integer and then, this program will display the fibonacci series of number from 0 to user specified number using Python For Loop

**PYTHON CODE**

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

**PYTHON CODE**

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

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

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

For the demonstration of Python 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 will end up in infinite execution (Same like infinite Loop).

Please be careful :)

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