Question

(TestSumSeries.java) Write a recursive method that sums up the

following series:

s(i) = 1/1+ 3/3+3/5+5/7+⋯+ (i+1)/(2i+1)+(i+2)/(2i+1) i = 0, 1, 2, 3, … When i is even, the term is (i+1)/(2i+1) When i is odd, the term is (i+2)/(2i+1) In the main method, display the s(i) for i = 0, 1, 2, 3, 4, 5

Answer 1

Code Segment:

import java.io.*;

public class TestSumSeries{
 // Recursive method to compute sum of the series
  public static double series_sum(int i)
  {    

       // if i becomes negative stop adding, return 0
       if(i<0)
       return 0;


      // if i is non-negative, do the computation    
       else

       {

       // if i is even 
       if(i%2==0)
       {   
           // add the term corresponding to even i 
           return((double)(i+1)/(2*i+1) + series_sum(i-1));
       }

       // if i is odd
       else
       {  // add the term corresponding to odd i
          return((double)(i+2)/(2*i+1) + series_sum(i-1));
       }


        }


  }


  public static void main(String[] args) {
  
        double result;
    
    // loop from 0 to 5
        for(int i=0; i<=5;i++)
        { 
         // calling the series_sum method for every i from 0 to 5
     result = series_sum(i);

     // printing the result
        System.out.println("s("    + i   + ") =  " + result);
        System.out.println();

    }

}

}

Output: