Tính nhanh: (1/2-1)(1/3-1)(1/4-1)...(1/999-1)

* Hướng dẫn giải

$\frac{5.18-10.27+15.36}{10.36-20.54+30.72}=\frac{5.18-\mathrm{5.18.3}+\mathrm{5.18.6}}{10.36-\mathrm{10.36.3}+\mathrm{10.36.6}}=\frac{5.18\left(1-3+6\right)}{10.36\left(1-3+6\right)}=\frac{1}{4}$