Round #1095

Compute the sum of the infinite geometric series 1 + 1/3 + 1/9 + 1/27 + ... Give the exact value.

```csharp using System; class Program { static void Main() { // Define the first term and common ratio double a = 1; double r = 1/3.0; // Calculate the sum of the infinite geometric series double sumSeries = a / (1 - r); Console.WriteLine(sumSeries); } } ```

```csharp public class GeometricSeriesCalculator { public static double CalculateGeometricSeriesSum(double a, double r) { if (Math.Abs(r) >= 1) { throw new ArgumentException("The series diverges because |r| is not less than 1."); } return a / (1 - r); } public static void Main(string[] args) { double a = 1; // First term double r = 1.0 / 3; // Common ratio double sum = CalculateGeometricSeriesSum(a, r); System.Console.WriteLine(sum); } } ``` This C# code calculates the sum of an infinite geometric series using the formula `a / (1 - r)`, where `a` is the first term and `r` is the common ratio. The `CalculateGeometricSeriesSum` method checks if the series converges by ensuring `|r| < 1`. If the series diverges, it throws an exception. The `Main` method demonstrates how to use this function to calculate the sum of the series `1 + 1/3 + 1/9 + 1/27 + ...`. The output will be `1.5`, which is the exact value of the series.