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Re: SumConvergence mistake?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg117906] Re: SumConvergence mistake?
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Sun, 3 Apr 2011 06:59:43 -0400 (EDT)

Sum[(-1)^k Log[k]/k, {k, 1, Infinity}] // Simplify

EulerGamma*Log[2] - Log[2]^2/2

% // N

0.159869

NSum[(-1)^k Log[k]/k, {k, 1, Infinity}]

0.159869


Bob Hanlon

---- Jon Joseph <josco.jon at gmail.com> wrote: 

=============
All: The following test for conditional convergence appears to give the wrong answer. By the Alternating Series test I think the sum should conditionally converge. Any comment or correction?

SumConvergence[(-1)^k Log[k]/k, k]

False (* I think should be true *)

and

SumConvergence[ Log[k]/k, k]

is correctly

False

Jon.



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