real analysis - Prove that $frac{1}{sqrt{2n-1}}-frac{1}{2n}geq frac{1}{2n}$ for $n = 1, 2, 3,...$

Prove that $\frac{1}{\sqrt{2n-1}}-\frac{1}{2n}\geq \frac{1}{2n}$ for $n = 1, 2, 3,...$

This is required to prove that the series $1-\frac{1}{2}+\frac{1}{\sqrt{3}}-\frac{1}{4}$ is divergent, but I don't know how to show this inequality to be true because the square root is present.