TIFR2010-Maths-B-1

Question

Let $U_{n}=\sin(\frac{\pi }{n})$ and consider the series $\sum u_{n}$. Which of the following statements is false?

• A. $\sum u_{n}$ is convergent
• B. $u_{n}\rightarrow 0$ as $n\rightarrow \infty $
• C. $\sum u_{n}$ is divergent
• D. $\sum u_{n}$ is absolutely convergent

Answer 1

https://math.stackexchange.com/questions/1413385/convergence-or-divergence-of-the-series-sum-limits-n-1-infty-sin-pi-n

Comments

make it comment or explain the solution so it helps.

---

The link is a reference and answer is not clear.(so i just posted it since nobody answered it here)