Sum of series $\;S=\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+\;....\;+\frac{1}{100\sqrt{99}+99\sqrt{100}} \;is$

Question

$(a)\;\frac{1}{10}\qquad(b)\;\frac{9}{10}\qquad(c)\;\frac{3}{10}\qquad(d)\;None$