Tính: 1/1.2+1/2.3+1/3.4....1/1999.2000

* Hướng dẫn giải

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