public class ConstantValue {
    public static void main(String[] args) {
        double term = 2, e = 0;
        final double difference = 0.0000000001; //or 1E-04

        for (int n = 0; term > difference; n++) {
            term = 1.0 / find_denominator(n);
            e += term;
		System.out.println("The Value of Constant e" + e);
        }
    }

    public static double find_denominator(int n) {

        if (n == 0 || n == 1)
            return 1.0;

        return n * find_denominator(n - 1);
    }
}

eazyd: Specially for @Javanian - love the way you code!

Javanian:
Am Flattered

public class ConstantValue{
	public static void main(String[] args){
		int k = 1;
		double term = k, e = 0;
		while(term > 1E-04){
			e += term;
			term = 1/compute(k++);
		}
		System.out.println("Constant e = " + e);
	}
	static double compute(int k){
		if(k==1)
			return k;
		return k * compute(k-1);
	}
}