Tính: 1 / 1.2 + 1/ 2.3 + 1 / 3.4 + ... + 1 / 2018.2019

* Hướng dẫn giải

$\begin{array}{l}\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\mathrm{...}+\frac{1}{2018.2019}=\frac{2-1}{1.2}+\frac{3-2}{2.3}+\mathrm{...}+\frac{2019-2018}{2018.2019}\\ =\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\mathrm{...}+\frac{1}{2018}-\frac{1}{2019}=1-\frac{1}{2019}=\frac{2018}{2019}\end{array}$