Tính:

- Hướng dẫn giải

$$\begin{gathered} \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\mathrm{...}+\frac{1}{1999.2000} \\ =\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\mathrm{...}+\frac{1}{1999}-\frac{1}{2000} \\ =1-\frac{1}{2000}=\frac{1999}{2000} \end{gathered}$$