Chapter 4, Problem 1E

Write a method called fractionSum that accepts an integer parameter n and returns as a double the sum of the first n terms of the sequence

$\sum \text{i}=1\text{n}1\text{i}$

In other words, the method should generate the following sequence:

$1+12+13+14+15+\cdots$

You may assume that the parameter n is nonnegative.

Explanation of Solution

Given code snippet:

  //define the static function

        public static double fractionSum(int n) {

            //declare the required variables

            int denominator = 1;

            double sum = 0.0;

            //loop to generate the sequence

            for (int i = 1; i <= n; i++) {

                //evaluate the value

                sum += (double) 1 / denominator;

                //increment the value

                denominator++;

            }

            //return statement

            return sum;

        }

Explanation to the above code snippet:

• In the above code, the static method named “fractionSum” is defined.
• Required variables are declared and initialized.
• For loop is initialized to generate the required sequence.
• Evaluate the value and store it in the variable “sum”.
• The value stored in the variable “sum” is returned.