I have to decide whether a the summation of a function over [1,infinty) converges or not.

A particular function is troubling me

$\displaystyle \frac{ln(n)}{n^3}$

I figured the Ratio test would be the best way to go about this. But I got

$\displaystyle \frac{a_{n+1}}{a_{n}} \rightarrow 1$

but seeing as 1 is not <1 or >1, so the test is inconclusive, yes?

Where would I proceed from here? Does this mean the limit does not exist, hence divergent?