Don't let the similarity of notation fool you! A rearrangement of a series is not the same as a subsequence. The sequence (n_k) would have to be strictly increasing in order to be a subsequence. The only way for this to happen, and to still be a rearrangement, is if n_k=k for all k. So in every other case, a rearrangement is completely different from a subsequence.

Analysis WebNotes by John Lindsay Orr.
Comments to the author: jorr@math.unl.edu

All contents copyright (C) 1996 John L. Orr
University of Nebraska--Lincoln
All rights reserved

Last modified: May 1996