calculus - Using nth Term Test to find if $cos(frac{1}{n})$ is divergent

So in this problem I'm required to use the nth term test for:

$$\sum_{n=1}^\infty\cos(\frac{1}{n})$$

I made it into:

$$\lim_{n\to \infty}cos(\frac{1}{n})$$

I think it's going to diverge because cosine oscillates, but I don't know how to prove it with the nth term limit that I have above. Would I just divide by $\frac{cos\frac{1}{n}}{\frac{1}{n}}$? I'm lost.

Answer

Since $$\lim_{n \rightarrow \infty} \cos (\frac{1}{n}) = \cos (0) = 1 \neq 0$$
then the series $$\sum_{n=1}^\infty\cos(\frac{1}{n})$$
will diverge.