infinite sum problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg52990] infinite sum problem*From*: marc <m9085.NOSPAM at yahoo.com>*Date*: Sat, 18 Dec 2004 04:00:59 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Hi, the following sum converges only for x<1, but Mathematica gives a result for general x when the sum is evaluated symbolically. In[1]:= Sum[(-1)^k*x^(2k),{k,0,Infinity}] Out[1]= \!\(1\/\(1 + x\^2\)\) In[2]:= Sum[(-1)^k*x^(2k),{k,0,Infinity}]/.x\[Rule]2 Out[2]= \!\(1\/5\) that's wrong! In[3]:= Sum[(-1)^k*2^(2k),{k,0,Infinity}] correctly gives error: Sum does not converge. Am I overlooking something? thanx, marc