bug in Sum?
- To: mathgroup at smc.vnet.net
- Subject: [mg38062] bug in Sum?
- From: Rob Pratt <rpratt at email.unc.edu>
- Date: Thu, 28 Nov 2002 14:08:21 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
In[1]:= Binomial[0,0]
Out[1]= 1
I agree.
In[2]:= Sum[Binomial[0,k],{k,0,0}]
Out[2]= 1
I agree again.
In[3]:= Sum[Binomial[0,k],{k,0,n}]
Out[3]= 0
I disagree. Should be If[n == 0, 1, 0].
In[4]:= Sum[Binomial[0,k],{k,0,Infinity}]
Out[4]= 0
I disagree. Should be 1.
In[5]:= Sum[Binomial[n,k],{k,0,Infinity}]
n
Out[5]= 2
I agree. But inconsistent with Out[4].
Perhaps my desired result for In[3] is expecting too much. After all, x/x
reduces to 1, not If[x == 0, Indeterminate, 1]. But Out[5] demonstrates
that Mathematica knows the binomial theorem. It ought to be able to come
up with the correct result for In[4].
Rob Pratt
Department of Operations Research
The University of North Carolina at Chapel Hill
rpratt at email.unc.edu
http://www.unc.edu/~rpratt/