Java Program to Find the Sum of Series 1 - x2/2! + x4/4! - x6/6! + …… xn/n!

In the previous article, we have discussed about Java Program to Print the Series x – x^3 + x^5 – x^7 + …… + N

In this article we are going to see how to find sum of the series 1 – x²/2! + x4/4! – x⁶/6! + ……. xⁿ/n! by using Java programming language.

Java Program to Find the Sum of Series 1 – x2/2! + x4/4! – x6/6! + …… xn/n!

On observing the pattern carefully, we can see

1^st no. Is always starts with 1
1^st no is assigned positive and the 2^nd no is assigned negative sign.

Example:

X = 2

N = 5

1 – 2²/2! + 2⁴/4! = 1-2+2/3 = -0.3333

Let’s see different ways to find sum of the series 1 – x²/2! + x4/4! – x⁶/6! + ……. xⁿ/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 – x2/2! + x4/4! – x6/6! + …… xn/n! By Using Loop

Approach:

Declare an int variable say ‘x’ which holds the number of whose we will be calculating the sum of the series.
Declare an int variable say ‘n’ which holds the last term value of the series.
Create Scanner class object.
Prompt the user to enter values for x and n.
Check if n is even or not, if not even then update it to nearest even no.
By using for loop find each 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 x ");
        int x = s.nextInt();
        // Taking input of number of elements in the series
        System.out.println("Enter the value of last exponent 'n' ");
        int n = s.nextInt();
        int a = 1;
        double sum = 0;
       // checking if n is even or not
        if (n % 2 != 0) 
        {
            n = n-1;
        }
       //for loop to print the series
       for (int i = 0; i <= n; i += 2) 
        {
            long b = 1;
            // to find factorial
            for (int j = 1; j <= i; j++) 
            {
                b *= j;
            }
            double t = Math.pow(x, i) / b * a;
            sum += t;
            a *= -1;
       } 
        System.out.println("Sum = " + sum);  
    }
}

Output:

Enter the value of x 
2
Enter the value of last exponent 'n' 
5
Sum = -0.33333333333333337

Method-2: Java Program to Find the Sum of Series 1 – x2/2! + x4/4! – x6/6! + …… xn/n! By Using While Loop

Approach:

Declare an int variable say ‘x’ which holds the number of which we will be calculating the sum of the series.
Declare an int variable say ‘n’ which holds the last term value of the series.
Create Scanner class object.
Prompt the user to enter values for x and n.
Check if n is even or not, if not even then update it to nearest even no.
By using while loop find each 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 x ");
        int x = s.nextInt();
        // Taking input of number of elements in the series
        System.out.println("Enter the value of last exponent 'n' ");
        int n = s.nextInt();
        int a = 1;
        double sum = 0;
       // checking if n is even or not
        if (n % 2 != 0) 
        {
            n = n-1;
        }
       //for loop to print the series
       int i = 0;
       while(i <= n) 
        {
            long b = 1;
            int j = 1;
            // to find factorial
            while(j <= i) 
            {
                b *= j;
                 j++;
            }
            double t = Math.pow(x, i) / b * a;
            sum += t;
            a *= -1;
            i += 2;
       } 
        System.out.println("Sum = " + sum);  
    }
}

Output:

Enter the value of x 
2
Enter the value of last exponent 'n' 
5
Sum = -0.33333333333333337

Method-3: Java Program to Find the Sum of Series 1 – x2/2! + x4/4! – x6/6! + …… xn/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 as value of “x”
Prompt the user to enter a number as value of “n”
Call a method to execute the sum series.
By using for loop find each 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 x ");
        int x = s.nextInt();
        //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(x,n);
   }
    public static void m1(int x, int n)
    {
        // initial no. Is 1
        int a = 1;
        double sum = 0;
       // checking if n is even or not
        if (n % 2 != 0) 
        {
            n = n-1;
        }
       //for loop to print the series
       for (int i = 0; i <= n; i += 2) 
        {
            long b = 1;
            // to find factorial
            for (int j = 1; j <= i; j++) 
            {
                b *= j;
            }
            double t = Math.pow(x, i) / b * a;
            sum += t;
            a *= -1;
       } 
        System.out.println("Sum = " + sum);  
    }
}

Output:

Enter the value of x 
5
Enter the value of last exponent 'n' 
10
Sum = -0.16274663800705413

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