Bài giải:

Đặt: A = $\frac{1}{2\times 4}+\frac{1}{4\times 6}+\frac{1}{6\times 8}+......+\frac{1}{96\times 98}+\frac{1}{98\times 100}$

   A = $\frac{1}{2}$  x ($\frac{2}{2\times 4}+\frac{2}{4\times 6}+\frac{2}{6\times 8}+......+\frac{2}{96\times 98}+\frac{2}{98\times 100}$)

   A = $\frac{1}{2}$ x ($\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+.....+\frac{1}{96}-\frac{1}{98}+\frac{1}{98}-\frac{1}{100}$ )

   A = $\frac{1}{2}$ x ($\frac{1}{2}-\frac{1}{100}$)

  A = $\frac{1}{2}$x $\frac{49}{100}$

  A = $\frac{49}{200}$