The series ∑n=1∞sin(n)n\sum_{n=1}^{\infty} \frac{\sin(n)}{n}∑n=1∞nsin(n) converges. Which test best justifies this convergence?
Alternating Series Test, since sin(n)\sin(n)sin(n) oscillates between −1-1−1 and 111
Dirichlet's Test: an=1/na_n = 1/nan=1/n decreases to 0, and partial sums of sin(n)\sin(n)sin(n) are bounded
Absolute Convergence Test: ∑∣sin(n)∣n\sum \frac{|\sin(n)|}{n}∑n∣sin(n)∣ converges
Ratio Test