# Interesting Limit (21)

Calculus Level 3

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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