#### Answer

The given series is divergent.

#### Work Step by Step

$\Sigma^{\infty}_{n=0} \frac{\pi^{n}}{3^{n+1}} = \Sigma^{\infty}_{n=0} \frac{\pi^{n}}{3^{n} \times 3^{1}}$
$=\Sigma^{\infty}_{n=0} \frac{1}{3} (\frac{\pi}{3})^{n}$
$a=\frac{1}{3}$ and $r=\frac{\pi}{3} \gt 1$
Since $|r| \gt 1$ the given series is divergent.