Answer
diverges
Work Step by Step
The nth partial sums are: $ s_n=(\sqrt 5 -\sqrt 4)+(\sqrt 6 -\sqrt 5)+.....[\sqrt {n+4} -\sqrt {n+3}]=(\sqrt{n+4}-2)$
Now, apply limits,we gwt $\lim\limits_{n \to \infty} s_n=\sqrt{n+4}-2=\infty$
This implies that when $s_n \to \infty$ as $n \to \infty$, thus, the g series is divergent.