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?
$$\sum_{n=1}^\infty \left(\sin\frac{1}{n}-\sin \frac{1}{n+1}\right)$$

$$\sum_{n=1}^\infty \left(\sin\frac{1}{n}-\sin \frac{1}{n+1}\right) = \left(\sin1-\sin \frac{1}{2}\right)+ \left(\sin\frac{1}{2}-\sin \frac{1}{3}\right)+\cdots+\left(\sin\frac{1}{n}-\sin \frac{1}{n+1}\right) = \sin1+\left(-\sin \frac{1}{2}+ \sin\frac{1}{2}\right)+\left(-\sin \frac{1}{3}+\cdots+\sin\frac{1}{n}\right)-\sin \frac{1}{n+1}=\lim_{n\to \infty} \left(\sin1-\sin \frac 1 n\right) = \sin 1$$
