حاصل عبارت$\frac{\sqrt{۲}-\sqrt{۱}}{\sqrt{۲}}+\frac{\sqrt{۳}-\sqrt{۲}}{\sqrt{۶}}+\frac{\sqrt{۴}-\sqrt{۳}}{\sqrt{۱۲}}+...+\frac{\sqrt{۹}-\sqrt{۸}}{\sqrt{۷۲}}$ کدام است؟
$\frac{\sqrt{2}-\sqrt{1}}{\sqrt{2}}+\frac{\sqrt{3}-\sqrt{2}}{\sqrt{6}}+\frac{\sqrt{4}-\sqrt{3}}{\sqrt{12}}+...+\frac{\sqrt{9}-\sqrt{8}}{\sqrt{72}}=\frac{6(\sqrt{2}-\sqrt{1})+\sqrt{12}(\sqrt{3}-\sqrt{2})+\sqrt{6}(\sqrt{4}-\sqrt{3})+...+(\sqrt{9}-\sqrt{8})}{\sqrt{72}}=\frac{6\sqrt 2-6+6-2\sqrt 6+2\sqrt 6-3\sqrt 2+...+3-2\sqrt 2}{\sqrt {72}}=\frac{6\sqrt 2-2\sqrt 2}{6\sqrt 2}=\frac{4\sqrt 2}{6\sqrt 2}=\frac{2}{3}$