Show that the following series diverges $$\sum^{\infty}_{n=1} \sin{\left(\frac{1}{n}\right)}.$$
We do this by the comparison test. Let $a_{n} = \sin{\left(\frac{1}{n}\right)}$ Now the only test I can really apply here in my opinion is the comparison test however i'm not really sure what to compare this to. I want to find some $b_{n}<a_{n}$ and show that this $b_{n}$ diverges.