what kind of test should I use to determine if this sequence converge or diverge? what kind of test should I use to determine if this sequence converge or diverge?
$$\sum_{n=1}^\infty \left(\sin\frac{1}{n}-\sin \frac{1}{n+1}\right)$$

By comparison test $$sin\frac{1}{n}-sin \frac{1}{n+1}=\\2sin(\frac{1}{n}-\frac{1}{n+1})cos(\frac{1}{n}+\frac{1}{n+1})=\\2sin(\frac{1}{n(n+1)})cos(\frac{2n+1}{n(n+1)})\\\leq2sin(\frac{1}{n(n+1)}) \\2\frac{1}{n(n+1)} \leq2 \frac{1}{n^2}\\$$then 
$$\sum sin\frac{1}{n}-sin \frac{1}{n+1} \leq \sum \frac{2}{n^2}$$
