Covergence test of $\sum_{n\geq 1}{\frac{|\sin n|}{n}}$
I need to prove that $$\sum_{n\geq 1}{\frac{|\sin n|}{n}}$$ is convergent.
How should I do it?
It is not convergent: $$ \frac{|\sin n|}{n}\ge\frac{\sin^2n}{n}=\frac12\Bigl(\frac1n-\frac{\cos(2\,n)}{n}\Bigr). $$
HINT Given any $4$ consecutive numbers, then at-least one of them will have $\vert \sin(n) \vert > 1/2$.