It would be nice if the user could say how many terms to sum up.
The user might want to see the sum of the first 10 terms, for example:
1/1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10
Here is the program again, with new blanks for the improvements.
Now the number of terms to sum up 
value() method:
import java.io.* ;
class HarmonicSeries
{
  double value( int ___________ )
  {
    int term=1 ;
    double sum = 0.0;
    
    while ( term <= ___________ )
    {
      sum += 1.0/term;           // add the next term to sum
      term++ ;                   // increment term
    }
    return sum;
  } 
}
class HarmonicTester
{
  public static void main ( String[] args ) throws IOException
  {
    BufferedReader stdin  = new BufferedReader( new InputStreamReader(System.in) );
    HarmonicSeries series = new HarmonicSeries();
    System.out.println("How many Terms?");
    int limit = Integer.parseInt( stdin.readLine() );
    System.out.println("Sum of " + limit + " terms:" + series.value( limit ) );
  }
}