Does ∑n=1∞sin2(n)n2\sum_{n=1}^{\infty} \frac{\sin^2(n)}{n^2}∑n=1∞n2sin2(n) converge?
Yes, by comparison with ∑1n2\sum \frac{1}{n^2}∑n21
No, it diverges
Yes, by ratio test
Inconclusive