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

 Search: Search body:
Forums (2)