Determine the set of real numbers x for which the following series diverges
$$\sum_{n=1}^{\infty}\left(\frac{1}{n}\csc\frac{1}{n}-1\right)^x$$
Determine the set of real numbers x for which the following series diverges
$$\sum_{n=1}^{\infty}\left(\frac{1}{n}\csc\frac{1}{n}-1\right)^x$$