Define the term Recursion? Give a recursive algorithm to find nth term of a Fibonacci series?

Recursion is a method of solving problems in computer science where the solution to a problem depends on solutions to smaller instances of the same problem. In programming, recursion is a process in which a function calls itself as a subroutine. This allows the function to be written in a much simpler form, and it can also manage tasks that would be complex, or even impossible, with other methods.

The basic idea behind recursion is that a problem is divided into smaller and simpler sub-problems until we reach a stage where the problem can be solved easily. The solution of all sub-problems is then combined to give the solution of the original problem.

Here is a simple recursive function to illustrate the concept:

def recursive_function(n):
    if n == 1:
        return 1
    else:
        return n * recursive_function(n-1)

In the above function, recursive_function is a recursive function as it calls itself.

Now, let's discuss the Fibonacci series and how to find the nth term of a Fibonacci series using a recursive algorithm.

The Fibonacci series is a series of numbers in which each number is the sum of the two preceding ones, usually starting with 0 and 1. That is, the sequence starts 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so forth.

The mathematical equation describing it is:

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

With seed values :

F(0) = 0, F(1) = 1

Here is a simple recursive algorithm to find the nth term of a Fibonacci series:

def fibonacci(n):
    if n <= 0:
        return "Input should be positive integer"
    elif n == 1:
        return 0
    elif n == 2:
        return 1
    else:
        return fibonacci(n-1) + fibonacci(n-2)

In the above function, fibonacci is a recursive function. It calls itself with arguments n-1 and n-2 until it reaches the base case (n == 1 or n == 2).

For example, if we want to find the 6th term of the Fibonacci series, we can call the function as follows:

print(fibonacci(6))  # Output: 5

This means that the 6th term of the Fibonacci series is 5.