Question

assuming n is a positive integer, the sum of the numbers from 1 to n can be defined recursively as follows: the sum from 1 to 1 is 1. the sum from 1 to n is n plus the sum from 1 to n-1. write a method named sum that has an int parameter, n, and recursively calculates and returns the sum of the numbers from 1 to n. the method should return the sum as an int. note: if the parameter n is 0 or negative, the sum method should return 0.

Answer 1

The 'sum' method calculates the sum of numbers from 1 to n using a recursive approach. It checks for base cases where n is less than or equal to 0 or equal to 1 before proceeding with recursion to calculate the sum.

Step-by-step explanation:

Assuming n is a positive integer, the sum of numbers from 1 to n can be defined recursively. The base case for the recursion is that the sum from 1 to 1 equals 1. For any other value of n, the sum from 1 to n is the value of n added to the sum of numbers from 1 to n-1. To handle edge cases where n is zero or negative, the method should return 0. Here's how one could write the sum method:

int sum(int n) {
if (n <= 0) {
return 0;
} else if (n == 1) {
return 1;
} else {
return n + sum(n - 1);
}
}

This code snippet demonstrates the recursive approach, which is a foundational concept in computer programming.

The sum of the numbers from 1 to n can be recursively calculated using the given formula. The base case is when n is 1, the sum is 1. Otherwise, the sum is n plus the sum of numbers from 1 to n-1. Here's an example: if n is 5, the sum would be 5 + the sum of numbers from 1 to 4.

To implement this recursively in a method named sum, you can check if n is 0 or negative, in which case the method should return 0. Otherwise, you calculate the sum by calling the sum method with n-1 as the parameter and adding n to it.