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