Tính a) 3/1.4 + 3/4.7 + 3/7.10 + ... + 3/40.43 b) 4/2.4 + 4/4.6 + 4/6.8

* Hướng dẫn giải

a) $\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+\mathrm{...}+\frac{3}{40.43}$$=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\mathrm{...}+\frac{1}{40}-\frac{1}{43}$$=1-\frac{1}{43}=\frac{42}{43}$

b) $\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+\mathrm{...}+\frac{4}{2016.2018}$ $=2\left(\frac{2}{2.4}+\frac{2}{4.6}+\mathrm{...}+\frac{2}{2016.2018}\right)$$=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\mathrm{...}+\frac{1}{2016}-\frac{1}{2018}\right)$$=2\left(\frac{1}{2}-\frac{1}{2018}\right)=\frac{1008}{1009}$