Chapter 1.5, Problem 2P

Use the preliminary test to decide whether the following series are divergent or require further testing. Careful: Do not say that a series is convergent; the preliminary test cannot decide this.

$\sqrt{2}+\frac{\sqrt{3}}{2}+\frac{\sqrt{4}}{3}+\frac{\sqrt{5}}{4}+\frac{\sqrt{6}}{5}+\mathrm{...}$