24: L'Hospital's rule yields

So the oscillating cosine is multiplied by numbers growing to infinity, which means that the sequence jumps up and down, sometimes it is a "big number times almost one", sometimes "a big number times almost negative one", so the points of the sequence will approach in turn infinity and negative infinity (but not in any decent and organized way, we know that sometimes cos(n) can be almost zero, so some terms of the sequence might be also quite small). The conclusion then is that the sequence is divergent, the limit DNE.

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