/*  T01n10.java -- This program computes the sum 1 + 0.5 + 0.25 + 0.125 + ...
 *  Notice that, after 25 terms are summed, the sum is
 *  reported to be exactly 2.  This is nonsense, mathematically speaking.
 *  The sum is merely very close to 2, and the precision of the float
 *  is too limited to show how close.
 *
 *  The real point of this example is to demonstrate the FOR loop.  This is
 *  a counter-controlled loop situation (the value of termNum, which is
 *  counting the number of iterations, is being used to determine when
 *  we have completed enough work), and FOR loops are typically used for
 *  such tasks.  We could have used a WHILE without any trouble, though;
 *  if you have some time, you might try rewriting the FOR loop as a WHILE
 *  loop, to help you understand their relationship.
 */

public class T01n10
{
    public static void main (String [] args)
    {
        final int NUM_TERMS = 25;   // Quantity of fractions to sum

        int   termNum = 1;  // identifier of the term currently considered
        float sum = 0,      // the running total of the fractions
              divisor = 1;  // denominator of current term; a power of 2

            /*  Note that in the following for loop, the initialization
             *  is empty.  We could have put the preceding initializations
             *  in there if we wished; in fact, that would be more
             *  in keeping with standard coding style.  But, it would 
             *  have made the for line really, really long; and it gives
             *  me the opportunity to show that the first component can
             *  be empty.
             */

        for ( ; termNum <= NUM_TERMS; termNum++, divisor *= 2)
        {
            sum += 1.0 / divisor;
            System.out.println("After adding term " + termNum 
                             + ", the sum is " + sum + ".");
        }
    }
}