Friday, June 22, 2018

limits - Prove that $lim limits_{n to infty} frac{x^n}{n!} = 0$, $x in Bbb R$.

Why is





$$\lim_{n \to \infty} \frac{2^n}{n!}=0\text{ ?}$$




Can we generalize it to any exponent $x \in \Bbb R$? This is to say, is




$$\lim_{n \to \infty} \frac{x^n}{n!}=0\text{ ?}$$








This is being repurposed in an effort to cut down on duplicates, see here: Coping with abstract duplicate questions.



and here: List of abstract duplicates.

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