Sum of Infinite Geometric Series

First term $a = 2\sqrt{2}$. Common ratio $r = \frac{4/\sqrt{3}}{2\sqrt{2}} = \sqrt{\frac{2}{3}}$. Sum $S = \frac{a}{1 - r} = \frac{2\sqrt{2}}{1 - \sqrt{\frac{2}{3}}} = \frac{2\sqrt{6}}{\sqrt{3} - \sqrt{2}}$. Rationalizing denominator: $S = 2\sqrt{6}(\sqrt{3} + \sqrt{2})$.