 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Sum of reciprocals (Posted on 2018-06-22) Evaluate the sum of reciprocals of double factorial of even nonnegative integers.

 No Solution Yet Submitted by Ady TZIDON No Rating Comments: ( Back to comment list | You must be logged in to post comments.) computer solution and research | Comment 1 of 2
DefDbl A-Z
Dim crlf\$

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 Please log in:

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