Re: Summation of Reciprocals of Primes

From: Luiz Henrique de Figueiredo (lhf_at_csgpwr1.uwaterloo.ca)
Date: 06/25/04 

Date: Fri, 25 Jun 2004 01:40:09 +0000 (UTC)

In article <42336979.0406241633.1e482640@posting.google.com>,
vernonner3voltazim <vnemitz@pinn.net> wrote:
>If those reciprocals are added up, will they converge on a particular value?
>Or will the sum grow forever?

As others have said, it grows forever.

On the other hand, the alternating sum of the reciprocals of primes
does converge (because every alternating series whose terms decrease to
zero converges). Unfortunately, no one knows an expression for the sum.
See
        http://www.research.att.com/projects/OEIS?Anum=A078437

This contrasts with the alternating sum of the reciprocals of natural numbers,
which converges to ln(2).
--lhf

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