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 \(\displaystyle \lim_{n\to \infty}\sqrt[n]{G_n}\).

Give your answer to 3 decimal places.

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