lim\lim\limits_{n \to{+}\infty}{\sqrt[n]{n!}} is infinite

How do I prove that \displaystyle\lim_{n \to{+}\infty}{\sqrt[n]{n!}} is infinite?

Answer

n! \geq (n/2)^{n/2} because half of the factors are at least n/2. Take n-th root.

Attribution
Source : Link , Question Author : Breton , Answer Author : sdcvvc

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