Alternating Series Test for Convergence Practice Test

Diverges because $\lim_{n\to\infty}\frac{\sin(1/n)}{n}\neq 0$.

Converges by the Alternating Series Test because $\frac{\sin(1/n)}{n}$ decreases for large $n$ and approaches $0$.

Converges because $\sin(1/n)$ is negative for large $n$.

Diverges because $\sin(1/n)$ oscillates.

Converges absolutely because $\sum \frac{\sin(1/n)}{n}$ converges.