What do you mean exactly by "a series is greater than another". It works if the are nonnegative numbers.
I was wondering whether one showing series is greater than another is sufficent to show if the former converges, so does the latter. Thats what I took the proof in the link to imply. Cauchy condensation test - Wikipedia, the free encyclopedia. But I've figured that must be wrong. So how does this proof justify convergence simply by noting one series is bigger than the other?
ok thanks for that. I am still confused about 2 things. One is that does not always exist so how does the implication work then. Second, the proof of the cauchy condensation theorem (on wikipedia) does not compare each term in with the corresponding term in so how does the proof work?