SeriesSum.java

Below is the syntax highlighted version of SeriesSum.java from §1.3 Conditionals and Loops.

/******************************************************************************
 *  Compilation:  javac SeriesSum.java
 *  Execution:    java SeriesSum n
 *
 *  Prints out the sum s = 1/1 + 1/4 + 1/9 + 1/16 + ...
 *  The series sums to pi^2 / 6 so sqrt(6 s) should be an approximation
 *  to pi = 3.1415926535897932384626.
 *
 *
 *  java SeriesSum 10
 *  3.04936163598207
 *
 *  java SeriesSum 100
 *  3.1320765318091053
 *
 *  java SeriesSum 1000
 *  3.1406380562059946
 *
 *  java SeriesSum 10000
 *  3.1414971639472147
 *
 *  java SeriesSum 100000
 *  3.141583104326456
 *
 *
 ******************************************************************************/

public class SeriesSum {

    public static void main(String[] args) {
        int n = Integer.parseInt(args[0]);

        double sum = 0.0;
        for (int i = 1; i <= n; i++) {
            sum += 1 / (1.0 * i * i);     // good - multiply by 1.0 to cast to double
            // sum += 1.0 / (i * i);      // bad  - overflow if n > 65,535
            // sum += 1 / (i * i);        // bad  - integer division
            // sum += 1.0 / i * i;        // bad  - computes (1.0 / i) * i
        }
        System.out.println(sum);
        System.out.println(Math.sqrt(6.0 * sum));
    }
}