AMGM!The AM-GM inequalityHere is the problem:

If with is convergent, then is always convergent? if not provide a counter example.

Now I don't think that it is also convergent. for example, . If I am right, what would be a counter example in terms of a? or anything else for that matter?

But if it is truly convergent, I know you have to approach this with the fact that a square root is non negative and you have to use a comparison test. but i just don't see how or why