Does the series ∑n=1∞sin(1n2)\sum_{n=1}^{\infty} \sin(\frac{1}{n^2})∑n=1∞sin(n21) converge?
Yes, by the Limit Comparison Test with ∑1n2\sum \frac{1}{n^2}∑n21
No, it diverges
Yes, by the Ratio Test
Yes, because sin(x)<x\sin(x) < xsin(x)<x