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TIFR2010-Maths-B-1

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

  1. $\sum u_{n}$ is convergent
  2. $u_{n}\rightarrow 0$ as $n\rightarrow \infty $
  3. $\sum u_{n}$ is divergent
  4. $\sum u_{n}$ is absolutely convergent
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