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Calculus Level 4

\[\large \lim_{n\to\infty} \sqrt[n^2]{{n \choose1}{n \choose 2}\cdots{n \choose n}}\]

Find the closed form of the limit above to 3 decimal places.

Notation: \(\displaystyle {n \choose k} = \dfrac {n!}{k!(n-k)!}\) denotes the binomial coefficient.

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