Tính tổng: 

- Hướng dẫn giải

$\begin{array}{l}1+\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\mathrm{...}+\frac{1}{2008.2009}\\ =1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\mathrm{...}+\frac{1}{2008}-\frac{1}{2009}\\ =1+1-\frac{1}{2009}=1\frac{2008}{2009}\end{array}$