sufficiently large k. A sequence is asymptotically periodic if its terms approach those of a periodic sequence. That is, the sequence x1, x2, x3, ... is asymptotically periodic if there exists a periodic sequence a1, a2, a3, ... for which For example, the sequence 1 / 3, 2 / 3, 1 / 4, 3 / 4, 1 / 5, 4 / 5, ... is asymptotically periodic, since its terms approach those of the periodic sequence 0, 1, 0, 1, 0, 1, .... References Sequences and series