r] has arithmetical duality when its recursive sequence, [RS.

r]([beta], n) be a recursive sequence of base p, with re R.

In our first example we present a simple recursive sequence graphically, with the aim to argue what the ultimate value (the limit) should be.

We present a geometric (graphical) method, as shown below in Figure 1, for students to develop a better understanding of the limit of the recursive sequence.

Beginning with nouns, a total of three prefixal recursive patterns emerge, which are exemplified below, together with a predicate containing the

recursive sequence in question:

Global attractivity in a rational

recursive sequence.

Li, Global attractivity in the

recursive sequence [x.

Elabbasy et al [5] investigated the global stability, periodicity character and gave the solution of a special case of the

recursive sequenceIn this paper we give some criteria to decide whether we can bound the tail of a

recursive sequence as in (1) by a polynomial term.

Abstract In this paper we investigate the boundedness, the periodic character and the global attractivity of the

recursive sequencek] behaviour of

recursive sequences, with applications to subgroup counting.

Considering in turn discrete-time modeling, continuous-time modeling, and spatial modeling, they cover stochastic

recursive sequences, Markov chains, stationary queues, the M/GI/1 queue, the Poisson process, the Markov process, systems with delay, loss systems, and spatial point processes.