尾递归-Java

Question

I am trying to create a method that is tail recursive and finds the sum of an equation ( i / 2i + 1 ) where i needs to increment 1-10 . I'm having trouble with how to reach the base case and make the recursion cease.

This is what I have so far:

public class SumSeries {

    public static void main(String[] args) {
        System.out.println(sumSeries());
    }

    public static double sumSeries(){
        int i = 10;

        if (i == 0)
            return 0;
        else
            return (i / (2 * i + 1));
    }
}

Answer 1

I think that you are looking something like that:

public class SumSeries {

    public static void main(String[] args) {
        System.out.println(sumSeries(10,0));
    }

    public static double sumSeries(int i,double result){

        if (i == 1)
            return result;
        else{
          double res = result + (i / (double)(2 * i + 1));
          return sumSeries(i-1,res);
       }
   }
}

Answer 2

If you want recursion, your method should look something like this:

public class SumSeries {

    public static void main(String[] args) {
        System.out.println(sumSeries());
    }

    // if you want to keep the argument-less method in main but want to calculate
    // the sum from 1 - 10 nevertheless.
    public static double sumSeries() {
      return sumSeries(10);
    }

    public static double sumSeries(int i){
        if (i == 0) {
            return 0;
        }
        else {
            // The cast to double is necessary. 
            // Else you will do an int-division here and get 0.0 as result.
            // Note the invocation of sumSeries here inside sumSeries.
            return ((double)i / (2 * i + 1)) + sumSeries(i-1);
        }
    }
}

Answer 3

If you're looking for a way to find this sum :

(1 / 2*1 + 1) + (2 / 2*2 + 1) + (3 / 2*3 + 1) + ... + i/(2i + 1)

You could try this :

public double sumSeries(int i) {
   if (i == 1) { // base case is 1 not 0
     return 1/3;
   } else {
     double s = i / (2.0 * i + 1.0);
     return s + sumSeries(i - 1);
   }
} 

Answer 4

Your method is not recursive. A recursive method needs to use 'himself' and at a certain condition it stops. An example:

public static double sumSeries(int x) { 
    if (x == 0)   
        return x;
    else {  
        return x + sumSeries(x - 1);
}

for your example, something like this would fit:

public static double sumSeries(double x) {
    if (x == 0)   
        return x;
    else  
        return (x / (2 * x + 1)) + sumSeries(x - 1.0); 
}

If I understood your algorithm correctly :) If not, edit the algorithm :)