لماذا يجب تعريف المتغير F كـdouble؟

import java.util.Scanner;
 
public class Factorial {
 
    public static void main (String[] args) {
 
        Scanner input = new Scanner(System.in);
 
        int N;
        double F;
        double S = 0;
 
        System.out.print("Enter a number For N : ");
        N = input.nextInt();
 
        for (int i=1; i<=N; i++)
        {
            F = 1;
            for (int k=1; k<=i; k++)
            {
                F = F * k;
            }
            S = S + ( 1/(i+F) );
        }
 
        System.out.print("S = " +S+ "\n");
 
    }
 
}