# Don't write all the possibilities, part 1

Algebra Level 4

Given $$y=\sqrt{x+\sqrt{x+\sqrt{x+...}}}$$, where $$x$$ is a natural number, what's the probability that $$y$$ will be a natural number, within the range $$1 \leq y \leq 2015$$? 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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