Question

I have to write a simple recursion method to calculate m(i) = (1/2) + (2/3) + ... + i/(i+1). I feel like this should be incredibly simple, but I cannot figure it out. I know that I have to loop by decrementing, but I just can’t get it. So far I have the following, which I know is completely wrong.

public class Recursion {
    public static void main(String[] args) {

        double n = run(10);
        System.out.print("Result: " + n);
    }

    public static double run(double nb) {
        double result = 0;

        if(nb == 2){
            return 1/2;
        }

        result += run(nb - 2) / run(nb - 1);
        return result;

    }

}

Answer 1

Use this recurrence relation:

m(i) = i/(i+1) + m(i-1)

In code, it might look like this:

public static double run(int i) {
    if (i < 1) {
        return 0;
    }
    return i / (i + 1.0) + run(i - 1);
}

Note that there’s no need for the argument to be floating point, just the return value.