Answer
Diverges
Work Step by Step
Here, we have the given series $\Sigma_{n=0}^{\infty} (\dfrac{2 \pi}{3})^n$
From the above series, we can see that the series shows a geometric series with common ratio $r=\dfrac{2 \pi}{3} \implies \dfrac{2 \pi}{3} \gt 1$.
Hence, we can conclude that the given series diverges.
