Java Program to Find the Sum of Series (x2 / 1!) + (x4 / 3!) + (x6 / 5!) + …… + N

In the previous article, we have discussed about Java Program to Find the Sum of Series 1 – x2/2! + x4/4! – x6/6! + …… xn/n

In this article we are going to see how to find sum of the series (x^2 / 1!) + (x^4 / 3!) + (x^6 / 5!) + … N by using Java programming language.

Java Program to Print the Series (x^2 / 1!) + (x^4 / 3!) + (x^6 / 5!) + … N

Let’s understand the series with an example.

Example:

Suppose the value of

X = 2
N = 5
Then series is like:
(2^2 / 1!) + (2^4 / 3!) + (2^6 / 5!) 
=> 4 + 16/6 + 64/120 = 7.2

Let’s see different ways to find sum of the series (x^2 / 1!) + (x^4 / 3!) + (x^6 / 5!) + … N

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

Method-1: Java Program to Find the Sum of Series (x2 / 1!) + (x4 / 3!) + (x6 / 5!) + …… + N By Using For 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 exponent value of the series.
Create Scanner class object.
Prompt the user to enter values for a and n.
By using for loop find term and keep track on its sum.
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();
        //for loop to print the series
        double sum = 0;
       for (int i = 2; i <= 2 * n; i += 2) 
        {
            long b = 1;
            for (int j = 1; j <= i - 1;  j++) 
            {
                b *= j;
            }
            double t = Math.pow(x, i) / b;
            sum += t;
        }
        System.out.println("Sum = " + sum);
    }
}

Output:

Enter the value of x 
2
Enter the value of last exponent 'n' 
5
Sum = 7.253615520282186

Method-2: Java Program to Find the Sum of Series (x2 / 1!) + (x4 / 3!) + (x6 / 5!) + …… + N By Using While 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 denominator value of the series
Create Scanner class object.
Prompt the user to enter values for a and n.
By using while loop find term and keep track on its sum.
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();
        //while loop to print the series
        double sum = 0;
        int i = 2;
        while(i <= 2 * n) 
        {
            long b = 1;
            for (int j = 1;j <= i - 1;j++) 
            {
                b *= j;
            }
            double t = Math.pow(x, i) / b;
            sum += t;
            i += 2;
        }
        System.out.println("Sum = " + sum);
    }
}

Output:

Enter the value of x 
2
Enter the value of last exponent 'n' 
5
Sum = 7.253615520282186

Method-3: Java Program to Find the Sum of Series (x2 / 1!) + (x4 / 3!) + (x6 / 5!) + …… + 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 for “x”
Prompt the user to enter the last denominator value for “n”
Call a method to execute the sum series
By using for loop find term and keep track on its sum.
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)
    {
        //for loop to print the series
        double sum = 0;
       for (int i = 2; i <= 2 * n; i += 2) 
        {
            long b = 1;
            for (int j = 1; j <= i - 1;  j++) 
            {
                b *= j;
            }
            double t = Math.pow(x, i) / b;
            sum += t;
        }
        System.out.println("Sum = " + sum);
    }
}

Output:

Enter the value of x 
5
Enter the value of last exponent 'n' 
10
Sum = 371.0160038182103

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