Series - in Java

Understanding the Series: 4.0, 16.0, and Beyond

Series - 4.0, 16.0, ..., n

In the realm of programming, generating sequences and series is a common exercise to understand loops, conditional statements, and mathematical operations. The provided Java code snippet is an excellent example of how to generate a specific numerical series: 4.0, 16.0, and so forth. Let's delve into the mechanics of the code and explore the underlying mathematical concept.

The Java Program

Here’s a breakdown of the provided Java code:

import java.util.Scanner;
import java.lang.Math; 

public class shounak {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in); 
        double a; 
        int i, n;
        System.out.print("Enter the number: ");
        n = sc.nextInt(); 
        for (i = 1; i <= n; i++) {
            if (i % 2 == 0) {
                a = Math.pow(i, 2); 
                System.out.println(a); 
            }
        }
        sc.close(); 
    }
}

Explanation of the Code

1. Import Statements:

   • import java.util.Scanner;: Imports the Scanner class for taking user input.

   • import java.lang.Math;: Imports the Math class to use mathematical functions, particularly Math.pow().

2. Main Method: The entry point of the program where execution begins.

3. Variable Declaration:

   • double a;: A variable to store the square of the number.

   • int i, n;: Loop counter i and the number n which is the upper limit provided by the user.

4. User Input: The program prompts the user to enter a number n. This determines how many terms in the series the program will evaluate.

5. Loop and Conditional Check:

   • for (i = 1; i <= n; i++): A loop that runs from 1 to n.

   • if (i % 2 == 0): Checks if i is even.

   • a = Math.pow(i, 2);: Computes the square of i when i is even.

   • System.out.println(a);: Prints the computed square.

6. Close Scanner: sc.close(); closes the scanner to prevent resource leakage.

The Series: 4.0, 16.0, and Beyond

The series generated by this code snippet consists of the squares of even numbers. Let's look at the mathematical basis:

• Even Numbers: Numbers divisible by 2, i.e., 2, 4, 6, 8, etc.

• Squares of Even Numbers: The series we obtain by squaring these even numbers is:

  • ( 2^2 = 4 )

  • ( 4^2 = 16 )

  • ( 6^2 = 36 )

  • ( 8^2 = 64 )

  • and so on...

Thus, the series is 4.0, 16.0, 36.0, 64.0, ..., which represents the squares of the even numbers starting from 2.

Output Example

If the user inputs 8, the program will generate the squares of all even numbers from 2 to 8:

Enter the number: 8
4.0
16.0
36.0
64.0

Conclusion

The given Java program effectively demonstrates how to generate a series of squares of even numbers using fundamental programming constructs. By understanding and modifying this basic template, one can explore a vast array of numerical sequences and deepen their grasp of both programming and mathematical principles.