Bài giải:

$\begin{align}& 1\frac{1}{3}\times 1\frac{1}{8}\times 1\frac{1}{15}\times 1\frac{1}{24}\times ........\times 1\frac{1}{99} \\ & =\frac{4}{3}\times \frac{9}{8}\times \frac{16}{15}\times \frac{25}{24}\times ...\times \frac{100}{99} \\ & =\frac{4\times 9\times 16\times 25\times ...\times 100}{3\times 8\times 15\times 24\times ...\times 99} \\ & =\frac{2\times 2\times 3\times 3\times 4\times 4\times 5\times 5\times ...\times 10\times 10}{3\times 2\times 4\times 3\times 5\times 4\times 6\times ...\times 9\times 11} \\ & =\frac{2\times 10}{11} \\ & =\frac{20}{11} \\\end{align}$