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javarecursionfractions
BluceRee
BluceRee

Reputation: 117

Adding fractions using recursion

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 ???;
}

Upvotes: 0

Views: 5682

Answers (2)

somethingShiny
somethingShiny

Reputation: 29

Does it need to be recursive? if not, a simple for loop will do the trick.

double sum = 0;
for(int x = 0; x < i; x++)
{
    sum += x / (2.0 * x + 1);
}
return sum;

If it must be recursive, you need to start by properly identifying the base case. In this situation, your base case could be either 0 or 1. Examples:

Base case is 0:

public static double m(int i)
{
    if(i==0)
        return 0;
    else
    { 
        double sum = i/(2.0 * i + 1);

        return sum + m(i-1);
    }
}

Base case is 1:

public static double m(int i)
{
    if(i==1)
        return 1.0/3.0;
    else
    { 
        double sum = i/(2.0 * i + 1);

        return sum + m(i-1);
    }
}

Upvotes: 0

thegrinner
thegrinner

Reputation: 12243

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);
  }
}

Upvotes: 3

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