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#### Alexmahone

##### Active member

- Jan 26, 2012

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Test for convergence: $\sum_1\sin\left(\frac{1}{n}\right)$

$\sin\left(\frac{1}{n}\right)\sim\frac{1}{n}$

Since $\sum_1\frac{1}{n}$ diverges, $\sum_1\sin\left(\frac{1}{n}\right)$ also diverges by the asymptotic convergence test.

Is that correct?

**:**__My attempt__$\sin\left(\frac{1}{n}\right)\sim\frac{1}{n}$

Since $\sum_1\frac{1}{n}$ diverges, $\sum_1\sin\left(\frac{1}{n}\right)$ also diverges by the asymptotic convergence test.

Is that correct?

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