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Why does Sum return 0 on this series?

• To: mathgroup at smc.vnet.net
• Subject: [mg82537] Why does Sum return 0 on this series?
• From: Adam Weyhaupt <aweyhau at siue.edu>
• Date: Wed, 24 Oct 2007 04:24:13 -0400 (EDT)

In Mathematica 6.0.1 on Mac OS X, Sum returns 0 on this series.

In[1]:= Sum[Log[n]^4/n^2, {n, 2, Infinity}]
Out[1]= 0
In[2]:= $Version
Out[2]= "6.0 for Mac OS X x86 (32-bit) (June 19, 2007)"

Of course that's not right, because the terms are all positive.  I  
don't expect Sum to always return a correct answer for any series  
(that would be unreasonable), and NSum is the more appropriate  
command to investigate this series numerically.  But 0 seems like a  
very strange answer.  Can anyone provide any insight on why  
Mathematica is returning 0 for the sum of a positive series?

Thanks,

Adam
-----
Adam Weyhaupt
	Department of Mathematics and Statistics
	Southern Illinois University Edwardsville
aweyhau at siue.edu
http://www.siue.edu/~aweyhau/
Science Building 1316	(618) 650-2220

• Follow-Ups:
  • Re: Why does Sum return 0 on this series?
    • From: Devendra Kapadia <dkapadia@wolfram.com>
  • Re: Why does Sum return 0 on this series?
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>