Calc II - How to find whether this ln sequence converges or diverges?

Question

Hi, I'm thrown off by the natural log in this problem.

Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit.

sequence = ln n^1/2 divided by n

How do I go about solving this problem? It's an even problem, so I don't have an answer to work toward.

Thanks! :>)

Answer 1

Well, ln (n^a) = a ln n, so you can pull out a factor of 1/2. And then you can forget about that factor, since you're just testing convergence ...

ln x/x goes to 0 is x goes to infinity. If you don't just KNOW that, then trot out L'Hopital's rule to prove it.

So the sequence converges, with limit 0.

Answer 2

An = (ln²n) / n lim n---> ?: ln²n / n lim n---> ?: ? / ? for the reason that we've ? / ?, we are able to apply L'Hopital's Rule.... lim n---> ?: (2 / n) / one million Plug in ? for all values of n..... very final answer: The sequence converges to 0.