Answer
Convergent
Work Step by Step
$\Sigma_{n=1}^{\infty}a_{n}=\Sigma_{n=1}^{\infty}\frac{1.3.5.....(2n-1)}{2.5.8.....(3n-1)}$
$\lim\limits_{n \to \infty}|\frac{a_{n+1}}{a_{n}}|=\lim\limits_{n \to \infty}|\dfrac{\frac{1.3.5.....(2n-1)(2n+1)}{2.5.8.....(3n-1)(3n+2)}
}{\frac{1.3.5.....(2n-1)}{2.5.8.....(3n-1)}}|$
$=\lim\limits_{n \to \infty}\frac{2n+1}{3n+2}$
$=\frac{3}{2}$
The series is convergent.