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!