Does this sequence tend to infinity?

a_n = n^4 |cos(n)|^4

Obviously it's unbounded but how can we tell if it goes to infinity or not? Am I right in thinking |cos(n)| can be infinitely small but never 0, since a natural number is never going to be a multiple of pi/2? And of course n^4 gets infinitely large so how can we decide if it goes to infinity, is there some clever trick? This is really bugging me!

Re: Does this sequence tend to infinity?

Re: Does this sequence tend to infinity?

Interesting, thanks for the reply. Out of interest, do you actually know the answer?

It's funny because I was writing random sequences on the board to see how well my tutees understood properties of sequences, and I realised I actually couldn't answer this one. My initial instinct was that it did tend to infinity, since it seems like we should be able to take n large enough to "counteract" the small values |cos(n)| can take. But I can see that this could easily be wrong if |cos(n)| can periodically take arbitrarily small values.