Determine the convergence of ∑n=1∞sin2(n)3n\sum_{n=1}^{\infty} \frac{\sin^2(n)}{3^n}∑n=1∞3nsin2(n).
Diverges; sin2(n)\sin^2(n)sin2(n) can be arbitrarily large
Converges; sin2(n)≤1\sin^2(n) \leq 1sin2(n)≤1 and ∑13n\sum \frac{1}{3^n}∑3n1 converges
Converges absolutely; by Limit Comparison Test
Diverges; by Limit Comparison Test to ∑1n\sum \frac{1}{n}∑n1