Hot topic: Limits

Calculus Level 5

\[\alpha= \displaystyle \lim_{n \to \infty} \left[ n \left( \frac{e^n n!}{n^{n+1/2} (\sqrt{2\pi})} -1 \right) \right]\]

If the above limit \(\alpha \) exists, find \(84\alpha\).

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