Investigating the behavior of the following series:
I broke it into 3 parts:
If $p = 0$ then it's just an infinite summation of ones, which diverges
If $p < 0$ then it diverges because log k goes to infinity as k goes to infinity
If $p > 0$ then it diverges by the integral test.
Is this right? Does it always diverge no matter what p is? Or did I do it wrong?