Java Program to Find the Sum of Series (1/1!) + (2/2!) + …… + (N/N!)

In the previous article, we have discussed about Java Program to Find the Sum of Series (x + (x^2/2!) + (x^ 3/3!) + …… + N term

In this article we are going to see how to find sum of the series (1/1!) + (2/2!) + …… + (N/N!) by using java programming language.

Java Program to Find the Sum of Series (1/1!) + (2/2!) + …… + (N/N!)

On observing the pattern carefully, we can see clearly that each term is like the number itself divided by the factorial of that number while the number starts from 1 and goes up to N. For example if the number is ‘a‘ then the term is like a/a!

Example:

N = 5

(1/1!) + (2/2!) +(3/3!) + (4/4!) + (5/5!)
=> 1/1 + 2/2 + 3/6 + 4/24 + 5/120
=> 1 + 1 + 0.5 + 0.17 + 0.042 = 2.72

Let’s see different ways to find sum of the series (1/1!) + (2/2!) + …… + (N/N!).

By Using for Loop
By using while Loop
By Using User Defined Method

Method-1: Java Program to Find the Sum of Series (1/1!) + (2/2!) + …… + (N/N!) By Using For Loop

Approach:

Declare an int variable say ‘n’ which holds the last term value of the series.
Create Scanner class object.
Prompt the user to enter a number as value of n.
Use a for loop from i=1 to i<=n
Inside loop find value of the term and keep track on sum of series.
Print the result

Program:

import java.util.*;
public class Main
{
    public static void main(String args[])
    {
        //creating object of Scanner class 
        Scanner s = new Scanner(System.in);
        //Taking input of number of elements in the series
        System.out.println("Enter the value of last exponent 'n' ");
        int n = s.nextInt();
        //for loop to print the series
       int fact=1;
        double sum=0;
       for(int i=1;i<=n;i++)
       {
        	fact*=i;
        	sum+=(double)i/fact;
       }
       System.out.println("Sum of the series is "+sum);
    }
}

Output:

Enter the value of last exponent 'n' 
5
Sum of the series is 2.708333333333333

Method-2: Java Program to Find the Sum of Series (1/1!) + (2/2!) + …… + (N/N!) By Using While Loop

Approach:

Declare an int variable say ‘n’ which holds the last term value of the series.
Create Scanner class object.
Prompt the user to enter a number as value of n.
Use a while loop and iterate from i=1 till i<=n
Inside loop find value of the term and keep track on sum of series.
Print the result

Program:

import java.util.*;
public class Main
{
    public static void main(String args[])
    {
        //creating object of Scanner class 
        Scanner s = new Scanner(System.in);
        //Taking input of number of elements in the series
        System.out.println("Enter the value of last exponent 'n' ");
        int n = s.nextInt();
        int i=1,fact=1;
        double sum=0;
        //using while loop to print the series
        while ( i <= n )
        {
   	   fact*=i;
           sum+=(double)i/fact;
     	   i++;
        }
        System.out.println("Sum of the series is "+sum);
    }
}

Output:

Enter the value of last exponent 'n' 
5
Sum of the series is 2.708333333333333

Method-3: Java Program to Find the Sum of Series (1/1!) + (2/2!) + …… + (N/N!) By Using User Defined Method

Approach:

The same logic as method 1 but this time we are moving the for inside a user-defined method
Create Scanner class object.
Prompt the user to enter a number “x”
Prompt the user to enter the last term value “n”
Call a method to execute the sum series
Use a for loop i<=n
Inside loop find value of the term and keep track on sum of series.
Print the result.

Program:

import java.util.*;
public class Main
{
    public static void main(String[] args)
   {
        // creating object of scanner class 
        Scanner s = new Scanner(System.in);
        //Taking input of number of elements in the series
        System.out.println("Enter the value of last exponent 'n' ");
        int n = s.nextInt();
        // calling m1 method to print the series
        m1(n);
   }
    public static void m1(int n)
    {
       //for loop to print the series
       double sum = 0;
       int fact=1;    
       for(int i=1;i<=n;i++)
       {
        	fact*=i;
        	sum+=(double)i/fact;
       }
       System.out.println("Sum of the series is "+sum);
    }
}

Output:

Enter the value of last exponent 'n' 
10
Sum of the series is 2.7182815255731922

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