The conversation between human and AI assistant.
Is [math]\displaystyle\sum_{n=1}^{\infty} 2 \sin\left(\frac{2}{n}\right) [/math] convergent or divergent?
How did you determine that?
I used the limit comparison test with [math]\displaystyle\sum_{n=1}^{\infty} \frac{1}{n}[/math] as the comparison series. The limit of the ratio of the two series is equal to 2, which is greater than zero. Therefore, the series is divergent.