arrow_back 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.