How to calculate Euler number in 1000 iteration?

Question

Is it possible to calculate Euler Number in 1000 iteration in one method and do I need to calculate factorial in the first place?

Here is my code:

import java.math.BigDecimal;

public class EulerNumber {

    public static void main(String[] args) {
        for (int i = 1; i < 1000; i++) { 
        }
        System.out.println("e = " + e);
    }

    private static double Euler() {
        return 0;
    }
}

Answer 1

It is pretty straight forward, if I understand it correctly, you need to calculate euler number in 1000 iteration, not calculating it 1000 times, so the for loop should be moved into Euler function.

public class EulerNumber {

    public static void main(String[] args) {
        System.out.println("e = " + Euler());
    }

    private static double Euler() {
        double e=1;
        double f=1;
        for ( int i=1; i <= 1000; i++) {
            f = f * (1.0 / i);
            if ( f == 0 ) break;
            e +=  f;
        }
        return e;
    }
}

e is the estimated euler number so far and f is the fraction to add in the next operation (1/n!). You don't have to calculate the n! each time, it is better to calculate it as you go on. I have checked and know that 1000 is too high for double precision, since f converge to 0 after 178 iteration in my computer. so the rest of process is not necessary.