This is the first of a probably numerous series (pun intended) of questions about complex series. My series work has never been good, and I don't write proofs well.
So here we go with the first:
I can't even think of an example that fits this situation, much less writing a proof for it. Any pointers (not full solutions please) would be appreciated.A point is said to be a limit point of a set E of points in the complex plane (as opposed to a sequence ) if every neighborhood of contains infinitely many (distinct) points of E. Show that a sequence can have a limit point in the sense that, given any the inequality holds for infinitely many points of , without being a limit point of the set of points corresponding to the terms of .