Find sum of factorials till N factorial (1! + 2! + 3! + … + N!)

Given a positive integer N. The task is to compute the sum of factorial from 1! to N!, 1! + 2! + 3! + … + N!.

Examples:

Input: N = 5
Output: 153
Explanation: 1! + 2! + 3! + 4! + 5! = 1 + 2 + 6 + 24 + 120 = 153.

Input: N = 1
Output: 1

Naive Approach: The basic way to solve this problem is to find the factorial of all numbers till 1 to N and calculate their sum.
Time Complexity: O(N^2) 
Auxiliary Space: O(1)

Approach: An efficient approach is to calculate factorial and sum in the same loop making the time O(N). Traverse the numbers from 1 to N and for each number i: 

• Multiply i with previous factorial (initially 1).
• Add this new factorial to a collective sum

At the end, print this collective sum.

Below is the implementation of the above approach.

C++

// C++ program to compute sum of series
// 1! + 2! + 3! + ... + N!
#include <iostream>
using namespace std;

// Function to return sum
// of 1!, 2! upto N!
int findFactSum(int N)
{
    // Initializing the variables
    int f = 1, Sum = 0;

    // Calculate the factorial and sum
    // in the same loop
    for (int i = 1; i <= N; i++) {

        f = f * i;
        Sum += f;
    }

    // Return Sum as the final result.
    return Sum;
}

// Driver Code
int main()
{
    int N = 5;

    // Function call
    cout << findFactSum(N);

    return 0;
}

Java

// Java code to implement above approach
class GFG {

    // Function to return sum
    // of 1!, 2! upto N!
    static int findFactSum(int N)
    {

        // Initializing the variables
        int f = 1, Sum = 0;

        // Calculate the factorial and sum
        // in the same loop
        for (int i = 1; i <= N; i++) {

            f = f * i;
            Sum += f;
        }

        // Return Sum as the final result.
        return Sum;
    }

    // Driver code
    public static void main(String[] args)
    {
        int N = 5;
        System.out.print(findFactSum(N));
    }
}

// This code is contributed ukasp.

Python3

# python program to compute sum of series
# 1! + 2! + 3! + ... + N!

# Function to return sum
# of 1!, 2! upto N!
def findFactSum(N):

    # Initializing the variables
    f = 1
    Sum = 0

    # Calculate the factorial and sum
    # in the same loop
    for i in range(1, N + 1):
        f = f * i
        Sum += f

    # Return Sum as the final result.
    return Sum

# Driver Code
if __name__ == "__main__":
    N = 5

    # Function call
    print(findFactSum(N))

    # This code is contributed by rakeshsahni

C#

// C# code to implement above approach
using System;
class GFG
{

  // Function to return sum
  // of 1!, 2! upto N!
  static int findFactSum(int N)
  {

    // Initializing the variables
    int f = 1, Sum = 0;

    // Calculate the factorial and sum
    // in the same loop
    for (int i = 1; i <= N; i++) {

      f = f * i;
      Sum += f;
    }

    // Return Sum as the final result.
    return Sum;
  }

  // Driver code
  public static void Main()
  {
    int N = 5;
    Console.Write(findFactSum(N));

  }
}

// This code is contributed by Samim Hossain Mondal.

Javascript

<script>
    // JavaScript code for the above approach

    // Function to return sum
    // of 1!, 2! upto N!
    function findFactSum(N)
    {

      // Initializing the variables
      let f = 1, Sum = 0;

      // Calculate the factorial and sum
      // in the same loop
      for (let i = 1; i <= N; i++) {

        f = f * i;
        Sum += f;
      }

      // Return Sum as the final result.
      return Sum;
    }

    // Driver Code
    let N = 5;

    // Function call
    document.write(findFactSum(N));

  // This code is contributed by Potta Lokesh
  </script>

Output:

153

Time Complexity: O(N) 
Auxiliary Space: O(1), since no extra space has been taken.