# Don't write all the possibilities, part 2

Algebra Level 5

Given $$y=\sqrt{x+\sqrt{x-\sqrt{x+\sqrt{x-\ldots}}}}$$, within the range $$1 \leq y \leq 2015$$:

Given that $$x$$ is a natural number such that $$1 \leq y \leq 2015$$, what is the probability that $$y$$ is a natural number?

Express the probability in the form $$\dfrac{a}{b}$$ (fraction in simplest form), and enter into the answer box the value of $$a+b$$.

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