I have to show that a sequence is convergent and I need to find their limits. So far so good, but this task has been giving me trouble:
$$z_n = 3^{-n}e^{in!}$$
It's clear that the $3^{-n}$ tends to 0, but I can't tell nearly as clearly what is going on in combination with $e^{in!}$. I want to intuitively say that everything tends to 0 because of $3^{-n}$, but I really doubt it and wouldn't be able to explain it outside of that anyway.
Help would be greatly appreciated!
Hint
$$|z_n|\leq \frac{1}{3^n}.$$