This critical value is $\alpha_0 \approx 1.3056867$ ... For $\alpha > \alpha_0$ the series converges, for $\alpha < \alpha_0$ it diverges.
Before the inexpensive computer, it was difficult to tell whether the critical value is ${}> 1$ or not.
This critical value is $\alpha_0 \approx 1.3056867$ ... For $\alpha > \alpha_0$ the series converges, for $\alpha < \alpha_0$ it diverges.
Before the inexpensive computer, it was difficult to tell whether the critical value is ${}> 1$ or not.