# Java Program to Find the Sum of Series (x + (x^2/2!) + (x^3/3!) + …… + N terms

In the previous article, we have discussed about Java Program to Find the Sum of Series (x2 / 1!) + (x4 / 3!) + (x6 / 5!) + …… + N

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

## Java Program to Find the Sum of Series (x + (x^2/2!) + (x^ 3/3!) + …… + N terms

Let’s understand the series with an example.

Example:

Suppose the value of
x = 2
N = 5
Then the series:
2 + (2^2 / 2!) + (2^3 / 3!) + (2^4 / 4!) +  (2^5/ 5!)
=> 2+ 4/2 + 8/6 + 16/24 + 32/120  =  2 + 2 + 1.34 + 0.67 + 0.27 = 6.28

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

### Method-1: Java Program to Find the Sum of Series (x + (x^2/2!) + (x^ 3/3!) + …… + N terms 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 term value of the series.
• Create Scanner class object.
• Prompt the user to enter values for x and n.
• Use a for loop from i=1 to i<=n.
• Inside loop find value of 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();
//for loop to print the series
int fact=1;
double sum=0;
for(int i=1;i<=n;i++)
{
double a=Math.pow(x,i);
fact*=i;
sum+=a/fact;
}
System.out.println("Sum of the series is "+sum);
}
}

Output:

Enter the value of x
2
Enter the value of last exponent 'n'
5
Sum of the series is 6.266666666666667

### Method-2: Java Program to Find the Sum of Series (x + (x^2/2!) + (x^ 3/3!) + …… + N terms 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 term value of the series
• Create Scanner class object.
• Prompt the user to enter values for x and n.
• Use a while loop from i=1 to i<=n
• Inside loop find value of 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();
//while loop to print the series
int fact=1;
double sum=0;
int i=1;
while(i<=n)
{
double a=Math.pow(x,i);
fact*=i;
sum+=a/fact;
i++;
}
System.out.println("Sum of the series is"+sum);
}
}

Output:

Enter the value of x
2
Enter the value of last exponent 'n'
5
Sum of the series is6.266666666666667

### Method-1: Java Program to Find the Sum of Series (x + (x^2/2!) + (x^ 3/3!) + …… + N terms 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 values for x and n.
• Call a method to execute the sum series by passing values of x and n as parameter.
• Use a for loop from i=1 to i<=n
• Inside loop find value of 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)
{
//for loop to print the series
int fact=1;
double sum=0;
for(int i=1;i<=n;i++)
{
double a=Math.pow(x,i);
fact*=i;
sum+=a/fact;
}
System.out.println("Sum of the series is"+sum);
}
}

Output:

Enter the value of x
5
Enter the value of last exponent 'n'
10
Sum of the series is145.38060102513225

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