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Re: Bug in Sum?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg109145] Re: Bug in Sum?
  • From: Erik Max Francis <max at alcyone.com>
  • Date: Mon, 19 Apr 2010 04:11:15 -0400 (EDT)
  • References: <hq0mqo$k1b$1@smc.vnet.net>

gopher wrote:
> In the following, A and Expand[A] give different answers after when
> summed (a finite geometric series.) The result of summing A is clearly
> wrong, since it is independent of the parameters r and s.
> 
> Abhishek
> 
> In[44]:= A = x^(i - n) (x^(i - n) (1 - r x^n) - s);
> A == Expand[A] // Simplify
> 
> Out[45]= True
> 
> In[46]:= Sum[A, {i, 0, n - 1}]
> 
> Out[46]= (x^(-2 n) (-1 + x^(2 n)))/(-1 + x^2)
> 
> In[47]:= Sum[Expand[A], {i, 0, n - 1}] // FullSimplify
> 
> Out[47]= -((
>  x^(-2 n) (-1 + x^n) (-1 + x^n (-1 + r + s + s x + r x^n)))/(-1 + x^2)
>  )

They're both equal.  FullSimplify on the first sum results in the same 
thing:

In[17]:= Sum[A, {i, 0, n - 1}] // FullSimplify

Out[17]= -((
  x^(-2 n) (-1 + x^n) (-1 + x^n (-1 + r + s + s x + r x^n)))/(-1 + x^2)
  )

By default Mathematica doesn't do a FullSimplify, so you end up with 
different, but equal answers.  If you do FullSimplify on both, then the 
answers are not only equal, but identical.

-- 
Erik Max Francis && max at alcyone.com && http://www.alcyone.com/max/
  San Jose, CA, USA && 37 18 N 121 57 W && AIM/Y!M/Skype erikmaxfrancis
   There is no fate that cannot be surmounted by scorn.
    -- Albert Camus


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