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Topic: sum(eulerphi(n)/n!,n=1...infinity) = 5*sqrt(Pi)/3 -1 ????
Replies: 6   Last Post: Feb 2, 2013 5:14 PM

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Rouben Rostamian

Posts: 17
Registered: 12/13/04
Re: sum(eulerphi(n)/n!,n=1...infinity) = 5*sqrt(Pi)/3 -1 ????
Posted: Feb 2, 2013 1:18 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In article <7f9f221a-67a3-420c-8119-ec9907dbb2ed@googlegroups.com>,
<apovolot@gmail.com> wrote:
>How close gets
>sum(eulerphi(n)/n!,n=1...infinity)
>to
>5*sqrt(Pi)/3 -1


For the sum of 20 terms Maple gives 84894610559376853 / 43444678717440000.
The difference from 5*sqrt(Pi)/3 -1 is approximately 0.000004393633187.
Repeating with 10,000 terms results in the same difference. So I guess
that answers your question.

--
Rouben Rostamian



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