先算出5!

    public static void main(String[] args) {
        int result = 1;
        int num = 1;
        while(num <= 5) {
            result *= num;
            num++;
        }
        System.out.println(result);
    }
    结果为120

再改动上面程序(加外层循环),算出1!+2!+3!+4!+5!

    public static void main(String[] args) {
        int a = 1;
        int result = 1;
        int num = 1;
        int sum = 0;
        while(a <= 5) {//算1~5的阶乘
            num = 1;//每一趟阶乘算完后,要重新之初始值
            result = 1;
            while(num <= a) {//算出a的阶乘
                result *= num;
                num++;
            }
            a++;
            sum += result;
        }
        System.out.println(sum);
    }