# Convergence/Divergence of $\sum_{n=1}^{\infty} \sin(1/n)$

it is a question Convergence/Divergence of calculus II! Please give me a hand!

Determine convergence or divergence using any method covered so far.

$$\sum_{n = 1}^{\infty} \sin (1/n)$$

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This looks like homework. What have you tried so far? Also, most of us probably don't know "methods covered so far", in your class. Perhaps you would care to state some of the things you are expected to use? –  Aryabhata Nov 11 '10 at 17:20

Hint: $\sin(x) / x \to 1$ as $x \downarrow 0$.

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You need to determine convergence for $\sum_{n=1}^\infty\sin(1/n)$. The series diverges. The two hints below may guide you when trying to justify this.
Hint 1: $\lim_{\theta\to0}\sin(\theta)/\theta=1$ and $1/n\to 0$ as $n\to\infty$.
Hint 2: $\sin(1/n)$ is positive. So you may attempt a limit comparison test.