#### Answer

Diverges

#### Work Step by Step

Consider $a_n=\dfrac{3^{n+2}}{ \ln n}$
Now, $l=\lim\limits_{n \to \infty} |\dfrac{a_{n+1}}{a_{n}} |=\lim\limits_{n \to \infty}|\dfrac{\dfrac{3^{n+1+2}}{ \ln (n+1)}}{\dfrac{3^{n+2}}{ \ln n}}|$
Thus, we have $l=\lim\limits_{n \to \infty}|\dfrac{3 \ln n}{\ln (n
+1)}|=3 \gt 1$
Hence, the series Diverges absolutely by the ratio test.