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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