Chapter 9 - Section 9.2 - Infinite Series - Exercises - Page 498: 40

Diverges

Here, $ s_n=(\sqrt 5 -\sqrt 4)+(\sqrt 6 -\sqrt 5)+.....[\sqrt {n+4} -\sqrt {n+3}]=\sqrt{n+4}-2$ Thus, we have $\lim\limits_{n \to \infty} s_n=\sqrt{n+4}-2=\infty$ We see that $s_n \to \infty$ as $n \to \infty$, so, the given series diverges.