# Java Program to Print the Sum of Series 1 + (x+2)/2! + (2x+3)/3! + (3x+4)/4! + ……  N

In the previous article, we have discussed about Java Program to Print Series 5 10 15 20 25 30 …N

In this article we are going to see how to print the Sum of Series 1 + (x+2)/2! + (2x+3)/3! + (3x+4)/4! + ……  N by using Java programming language.

## Java Program to Print the Sum of Series 1 + (x+2)/2! + (2x+3)/3! + (3x+4)/4! + …… N

In this series it can be seen that numbers at each position i, the term is calculated as ((i-1)x + i)/i!

For example:

For x = 2 at 3rd position the term is ((3-1)2 + 3)/3!=1.166666667

Here, for each we have to find the factorial of the number and add it to the sum.

Let’s see different ways to print the series.

### Method-1: Java Program to Print the Sum of Series 1 + (x+2)/2! + (2x+3)/3! + (3x+4)/4! + …… N By Using User Input Value

Approach:

• Create Scanner class object.
• Prompt the user to enter the value of x and n.
• Initialize the sum variable to 1 (as the first term in the series is always 1).
• Run a for loop from i=2 to n.
• Inside the loop, initialize variable f=1, which will hold the factorial.
• Use another nested loop from j=1 to i to find the factorial.
• Inside the nested loop, update f as f*= j.
• Outside the inner loop and inside the outer loop, initialize a variable as t = ((i - 1) * x + i) / (double)f, which will hold the current term.
• Then update sum as sum = sum + t.
• Print the sum outside the loops.

Program:

import java.util.Scanner;
public class Main
{
public static void main(String[] args)
{
// create scanner class object
Scanner sc = new Scanner(System.in);
// prompt user to enter x
System.out.print("Enter x: ");
int x = sc.nextInt();
// prompt user to enter n
System.out.print("Enter n: ");
int n = sc.nextInt();
double sum = 1;
// loop to calculate sum
for (int i = 2; i <= n; i++)
{
// finding factorial of n
double f = 1;
for (int j = 1; j <= i; j++)
{
f *= j;
}
// calculating the current term in the series
double t = ((i - 1) * x + i) / f;
// adding the current term to the sum
sum += t;
}
// print the result
System.out.println("Sum of the series is = " + sum);
}

}

Output:

Enter x: 2
Enter n: 3
Sum of the series is = 4.166666666666667

### Method-2: Java Program to Print the Sum of Series 1 + (x+2)/2! + (2x+3)/3! + (3x+4)/4! + …… N By Using User Defined Method

Approach:

Use the same approach as method 1 but move the nested loop to calculate the factorial inside a user-defined method.

Program:

import java.util.Scanner;
public class Main
{
public static void main(String[] args)
{
// create scanner class object
Scanner sc = new Scanner(System.in);
// prompt user to enter x
System.out.print("Enter x: ");
int x = sc.nextInt();
// prompt user to enter n
System.out.print("Enter n: ");
int n = sc.nextInt();
double sum = 1;
// loop to calculate sum
for (int i = 2; i <= n; i++)
{
// finding factorial of n
double f = fact(i);
// calculating the current term in the series
double t = ((i - 1) * x + i) / f;
// adding the current term to the sum
sum += t;
}
// print the result
System.out.println("Sum of the series is = " + sum);
}
// method to calculate factorial
private static double fact(int i)
{
double f = 1;
for (int j = 1; j <= i; j++)
{
f *= j;
}
return f;
}

}

Output:

Enter x: 2
Enter n: 3
Sum of the series is = 4.166666666666667

### Method-3: Java Program to Print the Sum of Series 1 + (x+2)/2! + (2x+3)/3! + (3x+4)/4! + …… N By Calculating Factorial Value Using Recursion

Approach:

Use the same approach as method 2 but the user-defined method will calculate the factorial value recursively.

• Define a method called fact which returns a double value take ‘n’ as an argument of int data type.
• Inside the recursive method, check if (n == 1), return 1 (base condition).
• Else return n*fact(n-1)

Program:

import java.util.Scanner;
public class Main
{
public static void main(String[] args)
{
// create scanner class object
Scanner sc = new Scanner(System.in);
// prompt user to enter x
System.out.print("Enter x: ");
int x = sc.nextInt();
// prompt user to enter n
System.out.print("Enter n: ");
int n = sc.nextInt();
double sum = 1;
// loop to calculate sum
for (int i = 2; i <= n; i++)
{
// finding factorial of n
double f = fact(i);
// calculating the current term in the series
double t = ((i - 1) * x + i) / f;
// adding the current term to the sum
sum += t;
}
// print the result
System.out.println("Sum of the series is = " + sum);
}

// method to calculate factorial recursively
private static double fact(double n)
{
// base condition
if (n == 1)
return 1;
return n * fact(n-1);
}

}

Output:

Enter x: 2
Enter n: 3
Sum of the series is = 4.166666666666667

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