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Limit of an Integer Function


I seem to have found a blind spot in my knowledge of how to get
Mathematica to evaluate limits.

I want to evaluate the limit of a function where the domain is a member
of the Natural numbers, such as infinite series.  It seems that Limit
assumes that the function is continuous.

For example, if I asked

Limit[Sin[ n Pi ],n-> Infinity], mathematica would return: 
Interval[{-1,1}].  This is true if n is a member of the Reals, but not
true if n is a positive integer (in which case the limit would be 0.]

Is there another function I should use?  Or would it be nice to specify
the domain of the function as a feature request?


Phil Mendelsohn


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