Question

1. [10 marks] (TestSumSeries.java) Write a recursive method that sums up the following series:

s(i) = 21+ 24+47+410+…+ i+23i+1+i+13i+1

i = 0, 1, 2, 3, …

When i is even, the term is i+23i+1

When i is odd, the term is i+13i+1

In the main method, display the s(i) for i = 0, 1, 2, 3, 4, 5

Answer 1

Implement the program as follows:

1. define the class TestSumSeries
2. define a static method CalcSum() that accepts integer, i
3. if i = 0, then return 1
4. if i is even, then recursively call CalcSum() and return i+23i+1 + CalcSum(i-1)
5. if i is odd, then recursively call CalcSum() and return i+13i+1 + CalcSum(i-1)
6. define main() method
7. for i varies from 0 to 5
8. print s(i) for i = 0, 1, 2, 3, 4, 5

Program: TestSumSeries.java

public class TestSumSeries{                                                                     /* define the class TestSumSeries */
        public static int CalcSum(int i){                                                       /* define a static method CalcSum() that accepts integer, i */
                if(i==0){                                                                                               /* if i = 0, then return 1 */
                        return 1;
                }
                else if(i%2==0){                                                                                /* if i is even, then recursively call CalcSum() and return i+23i+1 + CalcSum(i-1) */
                        return i+23*i+1 + CalcSum(i-1);
                }
                else{                                                                                                   /* if i is odd, then recursively call CalcSum() and return i+13i+1 + CalcSum(i-1) */
                        return i+13*i+1 + CalcSum(i-1);
                }
        }
        public static void main(String[] args){                                         /* define main() method */
                for(int i=0;i<6;i++){                                                                        /* for i varies from 0 to 5 */
                        System.out.println("s(" + i + ") = " + CalcSum(i)); /* print s(i) for i = 0, 1, 2, 3, 4, 5 */
                }
        }
}

Screenshot:

Output:

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