A calculus problem by Yuri Lombardo

Calculus Level 4

Determine the value of the limit below:

limn(2nn)n\lim_{n\to\infty} \sqrt[n]{ 2n \choose n}

Answer 666 if you think that the limit doesn't exist.

Notation: (MN)=M!N!(MN)! \dbinom MN = \dfrac {M!}{N! (M-N)!} denotes the binomial coefficient.

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