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.