Java Program to Find the Sum of Series 1 + (1/2!) + (1/3!) + (1/4!) + ……… + (1/n!)

In the previous article, we have discussed about Java Program to Find the Sum of Series x/2 + x/5 + x/8 + x/11 + …… + N

In this article we are going to see how to find sum of the series 1 + (1/2!) + (1/3!) + (1/4!) + … + (1/n!)) by using Java programming language.

Java Program to Find the Sum of Series 1 + (1/2!) + (1/3!) + (1/4!) + ……… + (1/n!)

On observing the pattern carefully, we can see

Numerator = 1 (fixed)

Denominator = starts from factorial 1 to n

Example:

N = 3

1 + (1/2!) + (1/3!) = 1 + 1/2 + 1/6 = 1+0.5+0.167 = 1.667

Let’s see different ways to find sum of the series 1 + (1/2!) + (1/3!) + (1/4!) + … + (1/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!) + (1/3!) + (1/4!) + ……… + (1/n!) By Using For Loop

Approach:

Declare an integer variable say ‘n’ which holds the value of “n“
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 the loop we will again use another for loop to find the factorial and then we will find the value of 1/fact and after that we will add it into sum for every iteration.
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 'n' ");
        int n = s.nextInt();
        //for loop to print the series
        double sum = 0.0;
        for (int i = 1; i <= n; i++) 
        {
            long fact = 1;
            for (int j = 1; j <= i; j++)
            {
                fact *= j;
            }
            sum += (1.0 / fact);
        }
        System.out.println("Sum of the series is " + sum);
    }
}

Output:

Enter the value of 'n' 
3
Sum of the series is 1.6666666666666667

Method-2: Java Program to Find the Sum of Series 1 + (1/2!) + (1/3!) + (1/4!) + ……… + (1/n!) By Using While Loop

Approach:

Declare an integer variable say ‘n’ which holds the value of “n“
Create Scanner class object.
Prompt the user to enter a number as value of n.
Use a while loop from i=1 to i<=n.
Inside the loop we will again use another while loop to find the factorial and then we will find the value of 1/fact and after that we will add it into sum for every iteration.
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 'n' ");
        int n = s.nextInt();
        //for loop to print the series
        double sum = 0.0;
        int i=1;
        while(i<= n) 
        {
            long fact = 1;
            int j=1;
            while(j <= i)
            {
                fact *= j;
                j++;
            }
            sum += (1.0 / fact);
            i++;
        }
        System.out.println("Sum of the series is " + sum);
    }
}

Output:

Enter the value of 'n' 
4
Sum of the series is 1.7083333333333335

Method-3: Java Program to Find the Sum of Series 1 + (1/2!) + (1/3!) + (1/4!) + ……… + (1/n!) By Using User Defined Method

Approach:

Create Scanner class object.
Prompt the user to enter the value “n”
Call a method to execute the sum series
Inside method use a for loop from i=1 to i<=n
Inside the loop we will again use another for loop to find the factorial and then we will find the value of 0 / fact and after that we will add it into sum for every iteration.
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)
        {
            double sum = 0.0;
            for (int i = 1; i <= n; i++) 
            {
                long fact = 1;
                for (int j = 1; j <= i; j++)
                {
                    fact *= j;
                }
                sum += (1.0 / fact);
            }
            System.out.println("Sum of the series is " + sum);
    }
}

Output:

Enter the value of last exponent 'n' 
10
Sum of the series is 1.7182818011463847

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