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Sum of reciprocals (Posted on 2018-06-22) Difficulty: 3 of 5
Evaluate the sum of reciprocals of double factorial of even nonnegative integers.

No Solution Yet Submitted by Ady TZIDON    
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Solution computer solution and research | Comment 1 of 2
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.

  Posted by Charlie on 2018-06-22 13:10:49
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