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Fibonacci Series

  • In Mathematics, Fibonacci Series or Fibonacci Numbers 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

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Python Fibonacci Series program Using While Loop

  • This Python 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 the Python While Loop

Sample 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
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OUTPUT

 Python Fibonacci Series program Using While Loop

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ANALYSIS

  • This 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, 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
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  • Let us see the working principle of this while loop in iteration wise.
  • 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, 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 so, program will start executing statements inside the while loop. 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 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

Sample 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)
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OUTPUT

 Python Fibonacci Series program Using For Loop

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  • We just replaced the While loop in the above 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 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.

Sample 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))
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OUTPUT

 Python Fibonacci Series program Using Recursion

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ANALYSIS

  • In this example we defined a function. Following function will accept integer values as parameter value and return value

def Fibonacci_series(Number):
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    • 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.
    • If the number is greater than 1 then the statements inside the else block will be executed.
  • Within the Else block we called the function recursively to display the Fibonacci series.
return (Fibonacci_series(Number - 2)+ Fibonacci_series(Number - 1))
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For example, 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).

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