[Axiom-developer] [#234 limit((-1/2)^n,n=%plusInfinity)] (new)

[anonymous]

Changes http://wiki.axiom-developer.org/234Limit12NNPlusInfinity/diff
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Another problem I have is that taking the limit of an expression
containing (-1)^n always returns "failed", where my TI-89 Titanium
calculator will give a finite limit.  For example:

 limit( 2 + (-2/%pi)^n, n=%plusInfinity )  ===> "failed"

... but the TI-89t returns 2.

The TI-89t says that the limit of (-1)^n as n approaches infinity is -1,
implying that it believes that infinity is an odd number.  That kind of
makes sense to me, since if you divide infinity in half, you still have
infinity, and you keep adding 1 to get to infinity, making it odd.  If
infinity is even then the answer should be 1, and if we can't know if
infinity is even or odd, then the answer is uncertain or undefined.

On the other hand, the TI-89t says that lim ( (-1)^n * (n + 1)/n ) is
undefined.  But it already told me that lim (-1)^n = -1, and that lim (n
+ 1)/n = 1.  If the limit of a product is the product of the limits of
the factors, then lim ( (-1)^n * (n + 1)/n ) should be -1, right?

So, who's right?
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