I want to use comparison test to test whether the following series are divergent or convergent. I found it easier to determine the convergent function, but have trouble dealing with divergent functions. Also, for normal integrals like second one, what is a good strategy to tell if it is convergent or divergent?
For (1) you only need to check in the interval $\;[1,\infty)\;$ (can you see why?) , and here
The same applies for the third case.
As for the second one on the given interval