The Program in  C# Program to Find Sum of series[ x-x^3+x^5-x^7+x^9-..] 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;
            int sign = 1;

            for (int i = 0; i < n; i++)
            {
                double factorial = 1;
                for (int j = 1; j <= 2 * i + 1; j++)
                {
                    factorial *= j;
                }

                sum += sign * Math.Pow(x, 2 * i + 1) / factorial;
                sign = -sign;
            }

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

Output:

Hello Codeauri Family, enter the value of X here:
8
Similarly, enter the number of terms in the series:
4
Okay, the sum of the series is: -220.368253968254

Pro-Tips💡

Here are the step by step execution of above program:

1. Read the value of X and the number of terms in the series from the user.
2. Initialize a variable ‘sum’ to store the sum of the series, and a variable ‘sign’ to keep track of the sign of each term in the series.
3. Start a loop from 0 to (n-1), where n is the number of terms in the series.
4. In the loop, calculate the factorial of (2 * i + 1) for each term.
5. Calculate the sum of each term by adding the value of (sign * x^(2 * i + 1) / factorial) to the ‘sum’ variable.
6. Reverse the sign of each term by assigning the opposite value to the ‘sign’ variable.
7. After the loop, print the final sum of the series.