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.

By Using User Input Value
By Using User Defined Method
By Using Recursion

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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