Answer
Diverges
Work Step by Step
$\lim _{k\rightarrow \infty }\dfrac {k}{\ln k}=\dfrac {\dfrac {\partial }{\partial k}\left( k\right) }{\dfrac {\partial }{\partial k}\left( \ln k\right) }=\dfrac {1}{\dfrac {1}{k}}=k=\infty \neq 0$
Then series diverges