Question

Write a recursive function that returns the sum of the even numbers 2 to n. All variables are to be declared and good programming practices are to be used inside the function. Assume the main program sends a positive integer into the function (you do not have to do any error checking on the input). Name the function SumOfEven. The function is called from some program (do not write this program, just the function) in a line like this: MySum = SumOfEven(n)

Answer 1

The SumOfEven function calculates the sum of even numbers from 2 to n using recursion. It adds the current even number to the sum if n is even, or skips to the next even number if n is odd, with a base case to terminate when n is less than 2.

Step-by-step explanation:

To write a recursive function called SumOfEven that returns the sum of the even numbers from 2 to a given positive integer n, you will need to follow a specific approach. The base case will be when n is less than 2, in which case the function should return 0. If n is an even number, you should add it to the result of the recursive call with n decremented by 2. If n is odd, you simply call the function with n decremented by 1 to get the next even number. Below is a possible implementation of the function in a generic programming language.

int SumOfEven(int n) {
if (n < 2) return 0; // Base case: no even numbers below 2
else if (n % 2 == 0) return n + SumOfEven(n - 2); // n is even, add it and recurse
else return SumOfEven(n - 1); // n is odd, skip it and recurse with n-1
}

The function works by checking whether the number n is even or odd. If even, it adds the number to the sum of all even numbers before it, which is obtained through the recursive call. If odd, it calls itself with n decreased by 1, hence moving to the next even number. This is a recursive approach to solve the problem that leverages good programming practices such as clear naming and a base case for termination.