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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 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 Codeint main(){    int N = 5;     // Function call    cout << findFactSum(N);     return 0;}

Java

 // Java code to implement above approachclass 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 Codeif __name__ == "__main__":    N = 5     # Function call    print(findFactSum(N))     # This code is contributed by rakeshsahni

C#

 // C# code to implement above approachusing 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



Output:

153

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

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