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>