# Here is the code:

```c#
namespace BKTest
{
    public class Pie
    {
        /// <summary>
        /// Estimates pi based on the number of fractions we desire it to estimate by.
        /// The way I view it: you basically have 4 * (element0 + element1 + element2 etc.)
        /// where element0, element1 etc are instances of the Element class.
        /// I use a factory method to instantiate the element types and use polymorphism to differentiate
        /// between the two different types of elements that are currently out there: Element0 and the others: Element1, Element2 etc .
        /// Element zero is different because you can't divide by zero! (This probably won't make any sense)
        /// Till you attempt the problem yourself.
        ///
        /// </summary>
        /// <param name="elementCount"></param>
        /// <returns></returns>
        public double Estimate(int elementCount)
        {
            ElementCollection ec = new ElementCollection(elementCount);
            return 4 * ec.AddAllElements();
        }
    }

    public class ElementCollection
    {
        private int elementCount;

        public ElementCollection(int elementCount)
        {
            this.elementCount = elementCount;
        }

        public double AddAllElements()
        {
            double result = 0.0;
            for (int i = 0; i < elementCount + 1; i++)
            {
                ElementN element = ElementFactory(i);
                result += element.Value();
            }

            return result;
        }

        public ElementN ElementFactory(int i)
        {
            if (i == 0)
            {
                return new Element0(i);
            }
            else
            {
                return new ElementN(i);
            }
        }

        public class Element0 : ElementN
        {
            public Element0(int elementCount)
                : base(elementCount)
            {
            }

            public override int Sign()
            {
                return 1;
            }

            public override double PosivitveValue()
            {
                return 1.0;
            }
        }

        public class ElementN
        {
            private int elementCount;

            public ElementN(int elementCount)
            {
                this.elementCount = elementCount;
            }

            virtual public double Value()
            {
                return Sign() * PosivitveValue();
            }

            virtual public double PosivitveValue()
            {
                return ((1.0) / (2.0 * elementCount + 1));
            }

            /// <summary>
            /// Either the sign is positive or negative
            /// We could probably put this into its own class
            /// and have a factory method but we'll keep it like this for the moment
            /// till one day change requires us to change it. After all, a sign can only
            /// either be positive or negative. (apparently you can also multiple by the
            /// square root of (-1) but that's another matter.
            /// </summary>
            /// <returns></returns>
            virtual public int Sign()
            {
                if (elementCount % 2 == 0)
                {
                    return 1;
                }
                else
                {
                    return -1;
                }
            }
        }
    }
}
```


# Here are the tests:

```c#
using NUnit.Framework;

namespace BKTest
{
    [TestFixture]
    internal class PieTest
    {
        [Test]
        [TestCase(0, 4)]
        [TestCase(1, 4 * (1 - 1.00 / 3.0))]
        [TestCase(2, 4 * (1 - 1.00 / 3.0 + 1 / 5.0))]
        [TestCase(3, 4 * (1 - 1.00 / 3.0 + 1 / 5.0 - 1 / 7.0))]
        [TestCase(4, 4 * (1 - 1.00 / 3.0 + 1 / 5.0 - 1 / 7.0 + 1 / 9.0))]
        public void Estimate_1Parameter_expect_fourMinusOneThird(int input, double output)
        {
            // set up
            double result = new Pie().Estimate(input);
            Assert.AreEqual(output, result);
        }
    }
}
```