Writing The Limit Of A Sequence With A Factorial

[Bashyboy]

Homework Statement

The sequence is $a_n = \frac{n^P}{e^n}$

Homework Equations

The Attempt at a Solution

If I did L'Hopital's rule P times, would the final product look like:

$P!\times lim_{n \rightarrow \infty} = \frac{1}{e^n}$ ?

 

[Dustinsfl]

Homework Statement

The sequence is $a_n = \frac{n^P}{e^n}$

Homework Equations

The Attempt at a Solution

If I did L'Hopital's rule P times, would the final product look like:

$P!\times lim_{n \rightarrow \infty} = \frac{1}{e^n}$ ?

I don't see why it wouldn't

 

[Bashyboy]

I just wasn't sure if I had wrote it properly. Thank you.