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Exercise 1

Write the recursive definition for the "Sum of Natural Numbers" problem. Make sure to include both a base case and a recursive definition.

Solution

In recursive problem-solving, we typically define two key components: a recursive definition and a base case. The recursive definition breaks down the problem into smaller instances of the same problem, while the base case provides a simple, non-recursive termination condition.

The Base Case

The base case in this scenario occurs when the number n is less than or equal to 1. In such cases, the sum of all natural numbers up to n is n itself. Although 0 is not traditionally a natural number, we include it here to handle edge cases effectively. This consideration is reflected in the last of our example test cases, where 0 is provided as input.

The Recursive Definition

In the case of summing the first n natural numbers, our recursive definition is as follows: The sum of the first n natural numbers can be expressed as n plus the sum of the first n-1 natural numbers.

The solution becomes more attainable with a well-defined base case and a recursive definition.

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