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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