本人是新手小白，求e的值，精确到小数点后第5位

public class Value_of_e {
    public static void main(String[] args){
        double e=1.0,n=1.0,i=n,m=n,j=n;
        while(n!=0){
            while(n!=1){
                n = n-1;
                i = i*n;
                }
            e = e+(m/i);
            n = j+1;
            j = n;
            m = n;
            i = n;
        }
        System.out.println(e);
    }
}
我是两个死循环套在一起的，我想要求极限，我要怎么从这两个循环里出来呢？
e=1+1/1!+2/2!+3/3!+~~~+n/n!