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## Homework Statement

$$\lim_{n \to \infty}\frac{10^n}{n!}$$

## Homework Equations

Do I need to use something as advanced as Stirling approximation?

This question appears in page 5 of Boas Mathematical Methods, there's no prior discussion on factorial or convergence test and etc.

## The Attempt at a Solution

I know the limit should be 0 because factorial got larger than power as n gets larger, but I'm not convinced with this treatment. What if it's not 10 but some arbitrary number. I've tried to write the terms and to cancel the factor but the sequence is still mainly irregular.

$$\frac{10}{1},\frac{50}{1},\frac{500}{3},\frac{1250}{3},\frac{2500}{3},\frac{12500}{9},...$$

Thank You

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