Function approaching... something

Calculus Level 3

Let $$p$$ be a function where for any positive $$x$$, $$p(x)$$ is $$\frac{x}{7}$$ rounded up to the nearest whole number. Evaluate:

$$\lim_{n \to \infty}p^{n}(x)$$

Where $$x$$ and $$n$$ are both ANY positive number.

Details and Assumptions

• $$p^{n}$$ means $$p$$ composed $$n$$ times, or $$p(p(p(p(...x)$$
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