Identify the convergence of ∑n=1∞sin2(n)n2\sum_{n=1}^{\infty} \frac{\sin^2(n)}{n^2}∑n=1∞n2sin2(n).
Converges by Comparison Test with ∑1/n2\sum 1/n^2∑1/n2
Diverges by the Test for Divergence
Converges by the Alternating Series Test
Diverges because sin2(n)\sin^2(n)sin2(n) oscillates