Answer
Diverges
Work Step by Step
Apply the root test.
Therefore, $ L=\lim\limits_{k \to \infty} |a_k|^{1/k}=\lim\limits_{k \to \infty} |(\dfrac{3k+2}{2k-1})^k|^{1/k}\\=\lim\limits_{k \to \infty} \dfrac{3k+2}{2k-1}\\=\lim\limits_{k \to \infty} \dfrac{3+2/k}{2-1/k}\\=\dfrac{3}{2} \gt 1$
So, we can conclude that the given series diverges by the root test.