We are given the sequence, and we need to check whether it is monotonic or not. I tried by showing that $\frac{a_{n+1}}{a_n} > 1$, and I came up that we need to show that $3\cdot(\frac{n}{n+1})^n > 1$. If we take the limit of this as $n$ approaches infinitive we get $e^{-1}$. So we get $\frac{3}{e} > 1$ which is correct. However, the textbook says that this sequence is not monotonic. Is the textbook wrong or I have done some mistake in my steps. Here is the sequence given.
$$a_n=\frac{3^n\cdot n!}{n^n}$$
