Not sure how to test this one:
Either my definition of from the series is wrong or the theorem should be:
So:
and
We obviously have that
so that part of the theorem is satisfied.
Now for
The constant term, of course, is immaterial here. The (-1) term simply oscillates between -1 and 1, so if the other part of the limit is zero then we're okay. And, in fact , so
as required.
-Dan