Answer
Diverges
Work Step by Step
Convergence of p-series Test: It states that the infinite series $\Sigma_{n=1}^{\infty}\dfrac{1}{n^p}$ converges if $p \gt 1$ and otherwise diverges.
Re-write the given series as: $\Sigma_{k=1}^{\infty} (k)^{-2/3}= \Sigma_{k=1}^{\infty}\dfrac{1}{k^{2/3}} $
We see that $\Sigma_{k=1}^{\infty}\dfrac{1}{k^{2/3}} $ has $p=\dfrac{2}{3} \lt 1$. This means that the given series diverges using p-series test.
