# A calculus problem by Anupam Khandelwal

Calculus Level 3

Given a sequence with the general term $$x_n = \dfrac{4n-5}{9n+2}$$. Let $$\displaystyle a = \lim_{n\to\infty} x_n$$ and let the number of terms $$x_n$$ lying outside the open interval $$(a-0.1, a +0.1)$$ be $$z$$. Find $$2z$$.

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