Answer
Divergent
Work Step by Step
Consider $f(x)=\dfrac{\ln x}{\sqrt x}$
Now, take the integral test to find the convergence and divergence for the sequence.
We have $\lim\limits_{a \to \infty} \int_2^a \dfrac{\ln x}{\sqrt x}dx= \lim\limits_{a \to \infty} [2 \ln xe^{\ln x/2} -4 e^{\ln x/2}]_{\ln 2}^a=\infty$
Hence, the sequence $\Sigma_{n=2}^\infty \dfrac{\ln n}{\sqrt n}$ is Divergent.
