Bài giải :

Ta có thể viết lại :

A = $\frac{1}{1\times (2\times 3)\times (3\times 2)}+\frac{1}{2\times (3\times 3)\times (4\times 2)}+\frac{1}{3\times (4\times 3)\times (5\times 2)}+...+\frac{1}{98\times (99\times 3)\times (100\times 2)}$

A = $\frac{1}{6}\times (\frac{1}{1\times 2\times 3}+\frac{1}{2\times 3\times 4}+\frac{1}{3\times 4\times 5}+...+\frac{1}{98\times 99\times 100})$

A x 12 = $\frac{2}{1\times 2\times 3}+\frac{2}{2\times 3\times 4}+\frac{2}{3\times 4\times 5}+...+\frac{2}{98\times 99\times 100}$

A x 12 = $(\frac{1}{1\times 2}-\frac{1}{2\times 3})+(\frac{1}{2\times 3}-\frac{1}{3\times 4})+(\frac{1}{3\times 4}-\frac{1}{4\times 5})+...+(\frac{1}{98\times 99}-\frac{1}{99\times 100})$

A x 12 = $\frac{1}{1\times 2}-\frac{1}{99\times 100}$ = $\frac{4949}{9900}$

A = $\frac{4949}{9900\times 12}=\frac{4949}{118800}$

Vậy A = 4949/118800