Let $U_{n}=\sin(\frac{\pi }{n})$ and consider the series $\sum u_{n}$. Which of the following statements is false?
- $\sum u_{n}$ is convergent
- $u_{n}\rightarrow 0$ as $n\rightarrow \infty $
- $\sum u_{n}$ is divergent
- $\sum u_{n}$ is absolutely convergent