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Let $A_n$ and $G_n$ denote the arithmetic mean and geometric mean of $\dbinom n0,\dbinom n1, \dbinom n2, \dots,\dbinom nn$ respectively.

Find $\displaystyle\lim_{n\to\infty} \sqrt[n]{\frac{G_n}{A_n}}$.

Resource: AMSS Summer Camp 2017.

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