How to find the sum of factorial of all numbers in a series?

Question

I want to create a program to find the sum of factorial of all numbers in a series till 20. I have to find 's' in s = 1 + (1*2) + (1*2*3) + ...(1*2*3...20). I tried a program but it is not working. I am using BlueJ IDE.

int a =1; 
    int s = 0;
    for(int i = 1; i <= 10; i++)
    {
        while (i >0)
        {

            a = a * i;
            i--;
        }
        s = s+a;
    }
    System.out.println(s);

The compiler does not show any error message but when I run the program the JVM(Java Virtual Machine) keeps loading and the output screen does not show up.

Answer 1

You should be using a different loop variable name in your inner loop, and you also need to use a long to store your sum. In fact, I would first write a method to multiply up to a number in the series. Like,

static long multiplyTo(int n) {
    long r = 1L;
    for (int i = 2; i <= n; i++) {
        r *= i;
    }
    return r;
}

Then you can invoke that and calculate your sum with a simple loop. Like,

long sum = 0L;
for (int i = 1; i <= 20; i++) {
    sum += multiplyTo(i);
}
System.out.println(sum);

I get

2561327494111820313

Answer 2

Using streams:

    long s = LongStream.rangeClosed(1, 20)
        .map(upper -> LongStream.rangeClosed(1, upper)
            .reduce(1, (a, b) -> a * b))
        .sum();
    System.out.println(s);

Prints 2561327494111820313

Answer 3

I did the same program using Scanner Class

import java.util.*;
class Sum_Factorial
{
    public static void main()
    {
        Scanner in = new Scanner(System.in);
        int i; //Denotes Integer
        int n; //Denotes Number
        int f=1; //Denotes Factorial
        int s=0; //Denotes Sum
        System.out.println("Enter the value of N : ");
        n=in.nextInt();
        for(i=1; i<=n; i++)
        {
            f=f*i;
            s=s+f;
        }
        System.out.println("Sum of the factorial numbers is "+s);
    }
}