Examples
The sequence of digits in the decimal expansion of 1/7 is periodic with period six:
- 1 / 7 = 0 . 1 4 2 8 5 7 1 4 2 8 5 7 1 4 2 8 5 7 ...
More generally, the sequence of digits in the decimal expansion of any rational number is eventually periodic (see below).
The sequence of powers of −1 is periodic with period two:
- −1, +1, −1, +1, −1, +1, ...
More generally, the sequence of powers of any root of unity is periodic. The same holds true for the powers of any element of finite order in a group.
A periodic point for a function ƒ: X → X is a point p whose orbit
is a periodic sequence. Periodic points are important in the theory of dynamical systems.
Read more about this topic: Periodic Sequence
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