public class Logarithmus {
    public static void main(String[] args) {

        double ln2 = 1d;
        int counter = 1;
        boolean pruef = false;
        double difference = 10000;

        while(difference > 0.0023) {
            counter++;
            if (counter % 2 == 1) {

                ln2 -= 1d - 1 / (float)counter;
                //ln2 = ln2 + 1 / (float)counter;

            }else {

                ln2 += 1d - 1 / (float)counter;
                //ln2 = ln2 - 1 / (float)counter;

            }


            difference = Math.log(2) - ln2;
if(difference < 0)
 difference *= -1;


        }

        System.out.println("Mit der Formel ln2 = " + ln2);
        System.out.println("Probe: Math.log(2) = " + Math.log(2));
        System.out.println("Abweichung des Ergebnis vom echten Wert um " + counter + " Stellen.");

    }


}