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From: leimkuhl@uiucdcsp.CS.UIUC.EDU
Newsgroups: net.math
Subject: Re: summation in closed form (2^k/k
Message-ID: <9600037@uiucdcsp>
Date: Sat, 7-Dec-85 17:44:00 EST
Article-I.D.: uiucdcsp.9600037
Posted: Sat Dec  7 17:44:00 1985
Date-Received: Tue, 10-Dec-85 06:31:37 EST
References: <7512@watdaisy.UUCP>
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Nf-ID: #R:watdaisy.UUCP:7512:uiucdcsp:9600037:000:759
Nf-From: uiucdcsp.CS.UIUC.EDU!leimkuhl    Dec  7 16:44:00 1985




 I think you should have checked your formula out before you post it.

  The formula you've posted is for Sum{ k / 2^k }  not Sum { 2^k / k}.

  I do not think there is a simple closed form.  The above is very
  simple to derive because Sum{ kx^k } = x Sum{ kx^(k-1) }
  = x derivative{ Sum{ x^k } }, which has a known simple closed form.
  The case x=.5 gives us the formula.  As I've pointed out in an
  earlier note, the actual problem involves integrating the formula
  for Sum{ x^k } (at least if we want a general formula) and this does
  not seem promising.  The Possibility exists that there is a simple
  closed form for Sum{ 2^k / k }, but not for Sum{ x^k / k }.  However,
  I see no reason why 2 should have such a distinction.

-Ben Leimkuhler