Answer
Converges
Work Step by Step
Apply a limit comparison test.
We have: $\lim\limits_{t \to \infty} \dfrac{t^{3/2}}{t^{3/2}-1}=1$
We also know that:
$\int_4^{\infty} \dfrac{2 dt}{t^{3/2}}=\lim\limits_{p \to \infty}\int_4^{p} \dfrac{2 dt}{t^{3/2}}$
and $\lim\limits_{p \to \infty}\int_4^{p} \dfrac{2 dt}{t^{3/2}}=\lim\limits_{p \to \infty}[-4/\sqrt x]_4^{p} =2$
Hence, the given integral converges by the limit comparison test.
