Groups > comp.soft-sys.math.mathematica > #1448

Re: SumConvergence mistake?

From	Bob Hanlon <hanlonr@cox.net>
Newsgroups	comp.soft-sys.math.mathematica
Subject	Re: SumConvergence mistake?
Date	2011-04-03 10:59 +0000
Organization	Steven M. Christensen and Associates, Inc and MathTensor, Inc.
Message-ID	<in9jv3$f98$1@smc.vnet.net> (permalink)

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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@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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Re: SumConvergence mistake? Bob Hanlon <hanlonr@cox.net> - 2011-04-03 10:59 +0000

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