Chinese problem

Calculus Level pending

Given a sequence with general term \(X(n) = \dfrac{3n-5}{9n+4} \). Find the number of integers \(n\) for which \(X(n) \) lying outside the open interval \(L = \left( \dfrac13 - \dfrac1{1000} , \dfrac13 + \dfrac1{1000} \right) \).

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