Question: Determine whether the series is convergent or divergent, and if it is possible, find the sum.

$\displaystyle \sum_{n = 1}\ln(\frac{n}{2n + 5})$

At this point in my class, we only know geometric series, the divergence test, and the p-series. So we cant use integral test, comparison test etc. My initial attempt was to use the divergence test. But I am having a hard time evaluating the limit. Thanks in advance.

p.s the sigma goes from n=1 to infinity.