24: The cosine oscillates, but here it is not compared to another term by means of adding/subtracting. Here the cosine is as a whole multiplied by some number (the ratio), that is, the oscillation cannot be overwhelmed by an added big number or something like that, it stays. The multiplication only affects the amplitude of the oscillation, that is, the size of each successive wave. So for the outcome it is crucial to find out where the fraction itself converges.
The fraction is actually a ratio of polynomials and similar powers, so one can handle it using appropriate tricks (factoring etc). Using the scale of powers one can actually guess right away that the ratio tends to infinity, since "powers beat logarithms".
However, this fraction is very simple and it is obviously of an indeterminate type ("infinity over infinity"), so probably the easiest way is to apply the l'Hospital rule.