Tính nhanh: B=1/9.10 - 1/8.9 - 1/7.8- ... - 1/7.8-1/1.2

* Hướng dẫn giải

Ta có:

 $$\begin{gathered} B=\frac{1}{9.10}-\left(\frac{1}{1.2}+\frac{1}{2.3}+\mathrm{...}+\frac{1}{7.8}+\frac{1}{8.9}\right) \\ = \frac{1}{9.10}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\right) \\ = \frac{1}{90}-\left(1-\frac{1}{9}\right) \\ =\frac{1}{90}-\frac{8}{9}=\frac{1}{90}-\frac{80}{90}=-\frac{79}{90} \end{gathered}$$

Vậy B = $-\frac{79}{90}$