The Program in C# Program to Display Sum of Series[ 1+x+x^2/2!+x^3/3!+..] is given below:

using System;

namespace SumOfSeries
{
    class Program
    {
        static void Main(string[] args)
        {
            Console.WriteLine("Hello Codeauri Family, enter the value of X here:");
            double x = double.Parse(Console.ReadLine());
            Console.WriteLine("Similarly, enter the number of terms in the series:");
            int n = int.Parse(Console.ReadLine());

            double sum = 0;

            for (int i = 0; i < n; i++)
            {
                double factorial = 1;
                for (int j = 1; j <= i; j++)
                {
                    factorial *= j;
                }

                sum += Math.Pow(x, i) / factorial;
            }

            Console.WriteLine("Okay, the sum of the series is: " + sum);
            Console.ReadLine();
        }
    }
}

Output:

Hello Codeauri Family, enter the value of X here:
3

Similarly, enter the number of terms in the series:
2
Okay, the sum of the series is: 4

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Here are the step by step execution of above program:

1. The program starts by importing the System namespace, which provides access to various classes and methods, including the Console class.
2. The program then declares a namespace SumOfSeries and a class Program within it.
3. The Main method is the entry point of the program and it contains the logic to display the sum of the series.
4. The program starts by displaying a message asking the user to enter the value of x.
5. The user input is read and parsed into a double variable x.
6. The program then displays another message asking the user to enter the number of terms in the series.
7. The user input is read and parsed into an int variable n.
8. The sum variable is declared and initialized to 0. This variable will store the sum of the series.
9. The program then enters a for loop that will run n times. This loop represents the terms of the series.
10. Within the loop, a factorial variable is declared and initialized to 1. This variable will store the factorial of the current term.
11. There’s another for loop that will run i times. This loop calculates the factorial of the current term.
12. In each iteration of the inner loop, the value of factorial is multiplied by j and then incremented.
13. After the inner loop, the value of x^i / factorial is added to sum.
14. After the outer loop, the final value of sum is printed using Console.WriteLine.
15. Finally, the program waits for the user to press the Enter key before ending.