/sci/ - Science & Math

How would someone go about showing the following limit is 1? The book presented this is obvious but I'm hoping someone could explain it better.
<span class="math"> \lim_{n \to +\infty} \frac{n!}{(n-a)}! \frac{1}{n^a}[/spoiler]
I know that <span class="math"> \frac{n!}{(n-a)!} \frac{1}{n^a} = \frac{(n)(n-1)(n-2)...(n-a+1)}{n^a}[/spoiler] but don't see how this equals 1. Wouldn't the bottom be a polynomial of degree a and the top be a polynomial of degree a-1?

How do I into category theory?
Nothing in the catalog that seems helpful.
I'm graduating in a couple weeks with a degree in math and chemistry and other than some stuff I picked up in my abstract algebra course I know nothing of category theory. When do people normally encounter it?
Pic absolutely unrelated

>>6460277

>>6264615
5/?
is my filename right?
I don't remember much from calc ii

>>6223548
i could fill a harddrive with em

here's one showing how a function (in this case e^x) can be represented as an infinite sum of its derivatives (taylor/maclaurin series). as n increases, the resultant function becomes a better and better approximation of e^x