a) Chứng tỏ rằng với 

- Hướng dẫn giải

$$\begin{gathered} a)\frac{1}{n(n+1)}=\frac{n+1-n}{n(n+1)} \\ =\frac{n+1}{n(n+1)}-\frac{n}{n(n+1)}=\frac{1}{n}-\frac{1}{n+1} \end{gathered}$$

$$\begin{gathered} b)\frac{1}{1.2}+\frac{1}{2.3}+\mathrm{...}\frac{1}{9.10} \\ =\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\mathrm{...}+\frac{1}{9}-\frac{1}{10}=\frac{9}{10} \end{gathered}$$