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Re: SumConvergence mistake?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg117905] Re: SumConvergence mistake?
  • From: DrMajorBob <btreat1 at austin.rr.com>
  • Date: Sun, 3 Apr 2011 06:59:32 -0400 (EDT)

You are right, and SumConvergence is wrong:

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

0.159869

Sum[(-1)^k Log[k]/k, {k, Infinity}]
N@%

1/2 (2 EulerGamma Log[2] - Log[2]^2)

0.159869

Bobby

On Sat, 02 Apr 2011 17:06:42 -0500, 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.


-- 
DrMajorBob at yahoo.com


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