When testing to determine the convergence or divergence of series with positive terms, there's a common way by comparing them with other series which we already know converge or diverge.
My question is, how do we choose the proper to-be-compared series? I hope to get some detailed methodology about this. I am a bit confused - do I have to even rely on my intuition?
For instance, how do I choose a comparison series for this given one below: