Adding fractions using recursion

Question

I need to write a recursive method to compute the following series:

m(i) = 1/3 + 2/5 + 3/7 + 4/9 + 5/11 + 6/13 + .... + i/(2i + 1)

Then I need to write a program that displays m(i) for i = 1,2,....10.

I understand the basic idea of recursion I had done 2 programs so far, one for factorials and one for a Fibonacci number sequence. This problem has me stumped.

This is what I have so far.

public static void main(String[] args) {
    for (int i = 1; i <= 10; i++) {
        System.out.println(m(i));
    }
}

public static double m(int i) {
    if (i == 1)
        return 1;
    else
        return ???;
}

Answer 1

First, it looks like your base case is off - that should be 1/3 (the first number in the series).

For your else, you should return the next step down added to the current step. Given your series, the current step is i/(2i + 1).

public static double m(int i) {
  if (i == 1) {
    // Base case is 1 - return the first number in the series
    return 1/3;
  } else {
    // Get the current step (ie the current iteration of m(i))
    double curStep = i / (2.0 * i + 1.0);

    // Return the current step plus the next step down
    return curStep + m(i - 1);
  }
}