lim-x-3-x-x-solution-

Question Number 190501 by 073 last updated on 04/Apr/23

\lim_{x \to \infty} \frac{3^{x}}{x!} = ?

solution ?

Answered by Frix last updated on 04/Apr/23

0

x! \sim \frac{x^{x}}{e^{x}} \sqrt{2 π x}

\frac{n^{x}}{x!} \sim \frac{n^{x} e^{x}}{x^{x} \sqrt{2 π x}} = {(\frac{3 n}{x})}^{x} \frac{1}{\sqrt{2 π x}} \sim 0 \forall n \in N^{★}

Commented by 073 last updated on 04/Apr/23

nice solution

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