S= 1/(1x2) + 1/(2x3) +........+ 1/(99x100)

* Hướng dẫn giải

$$\begin{gathered} = \frac{1}{1}- \frac{1}{2}+ \frac{1}{2} - \frac{1}{3}+ \frac{1}{3}- .............+ \frac{1}{99}- \frac{1}{100} \\ = 1-\frac{1}{99}=\frac{99}{100} \end{gathered}$$