Lecture 57:- Sum of Natural Number using Recursion

Certainly! Here's an example of a recursive function in Python that calculates the sum of natural numbers up to a given positive integer:

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def sum_of_natural_numbers(n):    if n == 1:        return 1    else:        return n + sum_of_natural_numbers(n - 1) # Test the function result = sum_of_natural_numbers(5) print(result)  # Output: 15

In this example, the sum_of_natural_numbers function uses recursion to calculate the sum of natural numbers up to n. It follows two essential steps of recursion: a base case to terminate the recursion and a recursive case to break down the problem into smaller subproblems.

When n is equal to 1, the function reaches the base case and returns 1. Otherwise, it adds n to the sum of natural numbers from 1 to n-1 by making a recursive call to sum_of_natural_numbers(n - 1). The recursive calls continue until the base case is reached, at which point the recursion starts to unwind, returning the accumulated sum.

In the example, sum_of_natural_numbers(5) returns the sum of natural numbers from 1 to 5, which is 15.

Recursion is a powerful technique, but it's important to ensure that the base case is properly defined and that the recursion terminates. Otherwise, it can lead to infinite recursion. Additionally, for large values of n, recursive solutions may hit recursion depth limits. In such cases, iterative or alternative approaches may be considered.