The Program in C# Program to Calculate the Value of e is given below:

using System;

namespace EulerCalculation
{
    class Program
    {
        static void Main(string[] args)
        {
            Console.WriteLine("Hello Codeauri Family, enter the number of decimal places to calculate e to:");
            int decimalPlaces = int.Parse(Console.ReadLine());
            double e = CalculateE(decimalPlaces);
            Console.WriteLine("e: " + e.ToString("F" + decimalPlaces));
        }

        static double CalculateE(int decimalPlaces)
        {
            double e = 1;
            double denominator = 1;
            for (int i = 1; i < decimalPlaces; i++)
            {
                denominator *= i;
                e += 1 / denominator;
            }
            return e;
        }
    }
}

Output:

Hello Codeauri Family, enter the number of decimal places to calculate e to:9
e: 2.718278770

Pro-Tips💡

Here are the step by step execution of above program:

1. using System; – This line includes the System namespace, which provides access to the Console class used to interact with the console.
2. namespace EulerCalculation – This line declares the EulerCalculation namespace, which is used to organize code and prevent naming collisions.
3. class Program – This line declares the Program class, which contains the logic of the program.
4. static void Main(string[] args) – This line declares the Main method, which is the entry point of the program. It takes an array of strings as an argument and returns nothing (void).
5. Console.WriteLine("Hello Codeauri Family, enter the number of decimal places to calculate e to:"); – This line writes a message to the console asking the user to enter the number of decimal places to calculate e to.
6. int decimalPlaces = int.Parse(Console.ReadLine()); – This line reads a line of text from the console and converts it to an integer, which is stored in the decimalPlaces variable.
7. double e = CalculateE(decimalPlaces); – This line calls the CalculateE method, passing it the decimalPlaces variable, and stores the result in the e variable.
8. Console.WriteLine("e: " + e.ToString("F" + decimalPlaces)); – This line writes the value of e to the console, formatted to the specified number of decimal places.
9. static double CalculateE(int decimalPlaces) – This line declares the CalculateE method, which takes an int argument and returns a double.
10. double e = 1; – This line initializes the e variable to 1.
11. double denominator = 1; – This line initializes the denominator variable to 1.
12. for (int i = 1; i < decimalPlaces; i++) – This line declares a for loop that will repeat decimalPlaces - 1 times. The loop variable i is initialized to 1 and incremented on each iteration.
13. denominator *= i; – This line updates the value of denominator by multiplying it by i.
14. e += 1 / denominator; – This line updates the value of e by adding 1 / denominator to it.
15. return e; – This line returns the value of e from the CalculateE method.