Use Mathematical Induction to Prove the Following Inequality for All $n \geq 2$

Essay

Use mathematical induction to prove the following inequality for all $n \geq 2$ .
$$\frac { 1 } { \sqrt { 2 } } + \frac { 1 } { \sqrt { 4 } } + \frac { 1 } { \sqrt { 6 } } + \ldots + \frac { 1 } { \sqrt { 2 n } } > \frac { \sqrt { n } } { \sqrt { 2 } }$$