# A Combinatorial Geometric Mean

Calculus Level 5

Let $$G_n$$ be the geometric mean of the following $$n+1$$ combinations:

$\displaystyle\binom{n}{0},\binom{n}{1},\binom{n}{2},\ldots,\binom{n}{n} .$

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