how to make dateadd in LINQ?

I do not know why your code is not working (Except see **1 below) but I am confident that it is not because of a malfunction in the AddDays() method, unless your installation has become corrupted.

I have just run some tests to make sure. I am checking for a 'test date' being between two other dates.

I created a simple Form containing:
2 NumericUpDown controls (nudStart and nudEnd) for defining the range of dates to check.
1 DateTimePicker (dateTimePicker1) for defining the 'test date'
1 Button (btnGo) to fire off the test
1 TextBox (txtResult - MultiLine on, WordWrap on) to display the outcome

Here is the code I used:

public partial class DateTimeTestForm : Form
{
    DateTime rangeStart = DateTime.MinValue;
    DateTime rangeEnd = DateTime.MaxValue;

    public DateTimeTestForm()
    {
        InitializeComponent();
    }

    private void ShowResult(bool isValid)
    {
        string resultString = "The test date {0:D} is{1} between {2:D} and {3:D}";

        this.txtResult.Text = string.Format(resultString, this.dateTimePicker1.Value,
            isValid ? "" : " NOT",
            rangeStart,
            rangeEnd);
    }

    private void btnGo_Click(object sender, EventArgs e)
    {
        ShowResult(this.dateTimePicker1.Value > rangeStart && this.dateTimePicker1.Value < rangeEnd);
    }

    private void nudStart_ValueChanged(object sender, EventArgs e)
    {
        this.rangeStart = DateTime.Now.AddDays((double)this.nudStart.Value);
    }

    private void nudEnd_ValueChanged(object sender, EventArgs e)
    {
        this.rangeEnd = DateTime.Now.AddDays((double)this.nudEnd.Value);
    }
}

If you want to try this for yourself you will need to hook up the event handlers, set nudStart to -56 and nudEnd to -49, select a date to test in the DateTimePicker (I did two tests 4th Feb 2011 and 8th Feb 2011) then click btnGo. You will see that AddDays() correctly sets the dates.

**1 I notice that you are checking for the PurchaseDate being outside of your date range. Is this what you intended?