Finding the Absolute convergence of a Series

Question

In this series I need to find whether it is absolutely convergent and im not so sure about my calculations
$$ \sum_{n=1}^\infty \left (\frac{-2n}{3n+5}\right)^n $$ the absolute value of this series is $$ \sum_{n=1}^\infty \Biggl|\left (\frac{-2n}{3n+5}\right)^n\Biggr| = \left (\frac{2n}{3n+5}\right)^n$$ and using the root test $$ \lim_{x\to\infty} \sqrt[n]{\left(\frac{2n}{3n+5}\right)^n} = \left(\frac{2n}{3n+5}\right)=\left(\frac{2}{3}\right) $$ and since $\left(\frac{2}{3}\right)$ is smaller then 1 by the root test the absolute value of the series is convergent and the original series is absolutely convergent? am I correct about this ?