Came across this in my maths book.
$$\lim_{n\to\infty} \frac{n!}{(n-k)!n^k} = 1$$
Why is it so?
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Some other posts about the same problem: Finding limit of sequence: $\lim _{n \to \infty} {\frac{n!}{n^k(n-k)!}}=1$, Proof that $\lim\limits_{h \to \infty} \frac{h!}{h^k(h-k)!}=1$ for any $k$, Limits involing Factorials $\lim_{N\to\infty} \frac{N!}{(N-k)!N^{k}}$, Why $ \lim_{n\rightarrow \infty} \frac{n!}{n^{k}(n-k)! } =1 $?, – Martin Sleziak Apr 13 '19 at 07:48