Determine all values of p for which the series is convergent, and express answer in interval notation.

$\displaystyle \sum_{n=2}^{\infty} (-1)^{n-1} \frac{ln(n)}{2n}^{p}$

How would I find the values of p that makes this series a convergent one. It appears to be an alternating series, so would I just focus on $\displaystyle \frac{ln(n)}{2n}^{p}$ ?

I am just not quite sure how to go about this problem. Could I used the ratio test or anything else?

Any feedback and help appreciated, thanks.