Program to find the sum of a Series 1/1! + 2/2! + 3/3! + 4/4! +…….+ n/n!

You have been given a series 1/1! + 2/2! + 3/3! + 4/4! +…….+ n/n!, find out the sum of the series till nth term.

Examples :

Input :n = 5
Output : 2.70833

Input :n = 7
Output : 2.71806

A simple solution is to one by one computer terms. For every term, find its corresponding factorial value.

An efficient solution is to do factorial computations in same loop.

CPP

filter_none

edit
close

play_arrow

link
brightness_4
code

// CPP program to print 
// the sum of series
#include<bits/stdc++.h>
using namespace std;
  
// function to calculate
// sum of given series
double sumOfSeries(double num)
{
    double res = 0, fact = 1;
    for (int i = 1; i <= num; i++)
    {
        // fact variable store 
        // factorial of the i
        fact = fact * i;
  
        res = res + (i / fact);
    }
    return(res);
}
  
// Driver Code
int main()
{
    double n = 5;
    cout << "Sum: " << sumOfSeries(n);
    return 0;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java program to print
// the sum of series
  
import java.io.*;
import java.lang.*;
  
class GFG
{
    public static double sumOfSeries(double num)
    {
        double res = 0, fact = 1;
        for (int i = 1; i <= num; i++)
        {
            // fact variable store
            // factorial of the i
            fact = fact * i;
  
            res = res + (i / fact);
        }
        return(res);
    }
  
    // Driver Code
    public static void main (String[] args)
    {
        double n = 5;
        System.out.println("Sum: " + sumOfSeries(n));
    }
}
  
// This code is contributed by 
// Mohit Gupta_OMG <(0_o)>

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python code to find smallest K-digit  
# number divisible by X
  
def sumOfSeries(num):
      
    # Computing MAX
    res = 0
    fact = 1
      
    for i in range(1, num+1):
        fact *= i
        res = res + (i/ fact)
          
    return res
      
  
n = 5
print("Sum: ", sumOfSeries(n))
  
# Code contributed by 
# Mohit Gupta_OMG <(0_o)>

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# program to print the sum of series
using System;
  
class GFG
{
    public static float sumOfSeries(double num)
    {
        float res = 0, fact = 1;
        for (int i = 1; i <= num; i++)
        {
            // fact variable store 
            // factorial of the i
            fact = fact * i;
  
            res = res + (i / fact);
        }
        return(res);
    }
  
    // Driver Code
    public static void Main ()
    {
        double n = 5;
        Console.Write("Sum: " + sumOfSeries(n));
    }
}
  
// This code is contributed by vt_m.

chevron_right


PHP

filter_none

edit
close

play_arrow

link
brightness_4
code

<?php
// PHP program to print
// the sum of series
  
// Function to calculate 
// sum of given series
function sumOfSeries($num)
{
    $res = 0; $fact = 1;
    for ($i = 1; $i <= $num; $i++)
    {
        // fact variable store 
        // factorial of the i
        $fact = $fact * $i;
  
        $res = $res + ($i / $fact);
    }
    return ($res);
}
  
// Driver Code
$n = 5;
echo("Sum: " . sumOfSeries($n));
  
// This code is contributed by Ajit.
?>

chevron_right



Output:

Sum: 2.70833

Time Complexity: O(n)

This article is contributed by R_Raj. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



My Personal Notes arrow_drop_up

Improved By : jit_t