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Bug in Sum?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg109109] Bug in Sum?
  • From: gopher <gophergoon at gmail.com>
  • Date: Mon, 12 Apr 2010 23:03:35 -0400 (EDT)

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)
 )


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