Answer
Diverges
Work Step by Step
Let us consider that $I_n=\int_2^n \dfrac{1}{\sqrt x} \ dx$
After integrating, we have: $I_n=2[\sqrt x]_2^n =2(\sqrt n-\sqrt 2)$
Now, $I=\lim\limits_{n \to \infty} I_n=\lim\limits_{n \to \infty} 2(\sqrt n-\sqrt 2) $
Since, $\sqrt n$ is unbounded.
Therefore, $I=\infty$
This means that the limit does not exist. So, the given integral diverges.
