Iterative Constructs in Java

Chapter 9

Iterative Constructs in Java

Class 10 - Logix Kips ICSE Computer Applications with BlueJ

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Java Program: Program to Calculate the Value of Pi Using Series

19. Write a program to calculate the value of Pi with the help of the following series:
Pi = (4/1) - (4/3) + (4/5) - (4/7) + (4/9) - (4/11) + (4/13) - (4/15) ...
Hint: Use while loop with 100000 iterations.

Program Title: Program to Calculate the Value of Pi Using Series

\[ \frac{4}{1} - \frac{4}{3} + \frac{4}{5} - \frac{4}{7} + \frac{4}{9} - \frac{4}{11} + \frac{4}{13} - \frac{4}{15} + \cdots \]

import java.util.Scanner;
 
class CalculatePi
{
    public static void main(String args[])
    {
        int i = 1, sign = 1;
        double pi = 0.0;
 
        while (i <= 100000 * 2)
        {
            pi = pi + (sign * 4.0 / i);
            sign = sign * (-1);   // Change sign
            i = i + 2;            // Next odd number
        }
 
        System.out.println("Value of Pi after 100000 iterations = " + pi);
    }
}
 

Sample Output
Value of Pi after 100000 iterations = 3.1415826535897198 

📝 Explanation

1. The program uses the Leibniz series to approximate the value of π.
2. Variable i starts from 1 and increases by 2 to generate odd numbers.
3. Variable sign alternates between +1 and −1 to handle addition and subtraction.
4. The loop runs 100000 iterations using a while loop as instructed.
5. Each term of the series is calculated as:

6. sign * 4 / i
7. The final value stored in pi is printed.