Rearrangement of Complex Series

This is an attempt at an exhaustive classification of infinite series whose terms are complex numbers, according to the manner of distribution of the limiting values of the series when the terms of the series are re-arranged so as to form another series. By the limiting values of the series are meant the limit points of the sequence obtained by taking the sum to first n terms of the series in any particular rearrangement. A definite arrangement of the terms of the series being presupposed, the series converges or diverges according as the sequence has a unique finite or infinite limit; otherwise the series oscillates.