C# Exercise: 66 Double, approximation of Pi

using System;  // Import the System namespace to use basic classes like Console

class Program  // Define the main class of the program
{
    static void Main()  // The entry point of the program
    {
        // Prompt the user for the number of terms
        Console.Write("Enter the number of terms to approximate Pi: ");
        int terms = int.Parse(Console.ReadLine());  // Read the user's input and convert it to an integer

        double piApproximation = 0.0;  // Variable to store the approximation of Pi

        // Loop through each term, adding or subtracting based on the formula
        for (int i = 0; i < terms; i++)  // Loop through the number of terms
        {
            // Calculate the current denominator (odd numbers: 1, 3, 5, 7, 9, ...)
            double denominator = 2 * i + 1;  
            
            // Use the formula to alternate adding and subtracting terms
            if (i % 2 == 0)  // If i is even, add the term
            {
                piApproximation += 1 / denominator;
            }
            else  // If i is odd, subtract the term
            {
                piApproximation -= 1 / denominator;
            }

            // Display the current approximation of Pi (multiply by 4 to get the approximation of Pi)
            Console.WriteLine($"After {i + 1} terms, approximation of Pi: {4 * piApproximation}");
        }
    }
}