## Calculus 8th Edition

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