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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