Answer
Diverges
Work Step by Step
Let us suppose a series $a_k$ such that $L=\lim\limits_{k \to \infty} |\dfrac{a_{k+1}}{a_k}|$ converges when $L\lt 1$ and diverges when $L \gt 1$
Now, we have: $ L=\lim\limits_{k \to \infty} |\dfrac{a_{k+1}}{a_k}|=\lim\limits_{k \to \infty} \dfrac{3^{k+1}}{(k+1)^2} \times \dfrac{3^k}{k^2}\\=\lim\limits_{k \to \infty} |\dfrac{3k^2}{(k+1)^2}| \\=3 \gt 1$
So, we can conclude that the given series diverges.
