Hello, and thanks for help in advance. I have an exam tomorrow that I'm very nervous about, so here goes:

I understand the justification for quite a few of the tests for convergence or divergence of series, such as the Comparison & Integral tests, but often have trouble applying any of them.

One example is the following:

If from n = 1 to n = infinity, is 1/(n + 4)^(1/2) convergent or divergent?

I understand that for p-series 1 / n^p, the function converges where p > 1 and diverges otherwise. Can I then say, because

1/(n + 4)^(1/2) ~ 1/(n)^(1/2) where 1/(n)^(1/2) diverges

that my original series (on left) diverges?

Are approximation methods like this (whether or not this one specifically works) allowed?