Recursive Fibonacci Series (Using Number)

# Our Objective

To implement a recursive function that generates the Fibonacci series(using Numbers).

# The Theory

The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding numbers. The sequence starts with 0, 1, and then the next number in the sequence is obtained by adding the previous two numbers. So the sequence goes: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on.

The function 'recur_fibo(n)' takes an integer 'n' as input and recursively calculates the n-th number in the Fibonacci sequence using the formula 'recur_fibo(n) = recur_fibo(n-1) + recur_fibo(n-2)'. The function returns the n-th Fibonacci number as an output.

The code first checks if the input 'nterms' (the number of terms to be printed in the sequence) is a positive integer. If nterms is not positive, it prints a message asking the user to enter a positive integer. Otherwise, it prints the Fibonacci sequence using a for loop that iterates nterms number of times, calling the 'recur_fibo()' function to generate each number in the sequence.

Note that while this implementation is simple and easy to understand, it is not the most efficient way to calculate the Fibonacci sequence for large 'n'. As 'n' gets larger, the number of recursive calls increases exponentially, leading to slow performance.

# Learning Outcomes

• Recursion: The code implements the Fibonacci sequence using recursion, which is a powerful programming technique that allows a function to call itself. By understanding this code, one can learn the basics of recursion, including how to write a function that calls itself and how to solve problems using recursion.
• Input validation: The code checks whether the input nterms is a positive integer and prints an error message if it is not. By understanding this code, one can learn how to check for input validity and handle user input errors.
• Looping: The code uses a for loop to iterate through a sequence of numbers and call the recur_fibo() function to generate each number in the Fibonacci sequence. By understanding this code, one can learn how to use loops to iterate through a sequence of data and perform operations on each item in the sequence.
• Problem-solving skills: The Fibonacci sequence is a classic example of a problem that can be solved using recursion. By understanding this code, one can develop problem-solving skills and improve algorithmic thinking.