SUM, from 1 to infinity of:

ln(n)

________

(n+1)^3

I work this out using the ratio test for convergence and the answer I get is "1"...

Does this sound right?

No, it doesn't. The ratio test acually tells you that this series converges absolutely:

\(\displaystyle \frac{a_{n+1}}{a_n}=\frac{\ln(n+1)}{\ln (n)}\cdot\frac{n^3}{n^3+3n^2+3n+1}\rightarrow 0\)

The first factor goes to 1 as n goes to \(\displaystyle \infty\), since

\(\displaystyle \frac{\ln(n+1)}{\ln (n)}=\frac{\ln(n)+\ln(1+1/n)}{\ln(n)}\)

and the second factor goes to 0.

If so, this then means that there are no other tests that can be done correct?

No: if the ratio test fails, the root test might still be used to prove absolute convergence.