For which real values of α\alphaα does the series ∑n=1∞(sin(1nα)−1nα)\sum_{n=1}^{\infty} \left( \sin\left(\frac{1}{n^\alpha}\right) - \frac{1}{n^\alpha} \right)∑n=1∞(sin(nα1)−nα1) converge?
α>1/3\alpha > 1/3α>1/3
α>1\alpha > 1α>1
α>1/2\alpha > 1/2α>1/2
α>0\alpha > 0α>0