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Let $\gamma>1$ be a real number and let $n\in \mathbb{N}$. Define $f\colon\mathbb{N}\to[0,1]$ $$ f(n_0) = \frac{\binom{n-n_0}{m}}{\binom{n}{m}}, $$ where $$ m = \Big\lfloor{\frac{n}{\lceil\gamma ...