DefDbl A-Z

Dim crlf$

Private Sub Form_Load()

 Form1.Visible = True

 Text1.Text = ""

 crlf = Chr(13) + Chr(10)

 

 n = 2: df = 2: tot = 1 / 2

 For i = 4 To 300 Step 2

   df = df * i

   tot = tot + 1 / df

 Next

 

 Text1.Text = Text1.Text & crlf & tot & " done"

  

End Sub

finds numerically the value  .648721270700128. But to this we must add 1, as the puzzle asks for inclusion of values for non-negative even numbers rather than for positive even numbers and the double factorial of zero is 1. So the actual value would be approximated by 1.648721270700128.

A Dictionary of Real Numbers, by Jonathan and Peter Borwein, identifies this as sqrt(e). Taking the square root of e verifies this is the case, as the book is catalogued by the portion after the decimal--the same value as found by the program.