# 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

• 1st no. Is always starts with 1
• 1st no is assigned positive and the 2nd 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!

### 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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