$\frac{4}{2 x 4}$ + $\frac{4}{4 x 6}$  + $\frac{4}{6 x 8}$  + $\frac{4}{8 x 10}$ +...+$\frac{4}{16x 18}$  + $\frac{4}{18 x 20}$ 

= $\frac{2}{2}$ x ($\frac{4}{2 x 4}$ + $\frac{4}{4 x 6}$  + $\frac{4}{6 x 8}$  + $\frac{4}{8 x 10}$ +...+$\frac{4}{16x 18}$  + $\frac{4}{18 x 20}$)

=  $\frac{4}{2}$ ($\frac{2}{2 x 4}$ + $\frac{2}{4 x 6}$  + $\frac{2}{6 x 8}$  + $\frac{2}{8 x 10}$ +...+$\frac{2}{16x 18}$  + $\frac{2}{18 x 20}$ )

= $\frac{4}{2}$ ($\frac{1}{2}$ - $\frac{1}{4}$ + $\frac{1}{4}$ - $\frac{1}{6}$  + $\frac{1}{6}$ - $\frac{1}{8}$ + $\frac{1}{8}$ - $\frac{1}{10}$ + ... + $\frac{1}{16}$ - $\frac{1}{18}$ + $\frac{1}{18}$ - $\frac{1}{20}$ 

= $\frac{4}{2}$ ($\frac{1}{2}$ - $\frac{1}{20}$)

= $\frac{4}{2}$ x $\frac{9}{20}$

= $\frac{9}{10}$

Đặt $A=\dfrac{4}{2\times4} + \dfrac{4}{4\times6} + ...... + \dfrac{4}{16 \times 18} + \dfrac{4}{18 \times 20}$

$A:4 = \dfrac{1}{2\times4} + \dfrac{1}{4\times6} + ...... + \dfrac{1}{16 \times 18} + \dfrac{1}{18 \times 20}$

$A:4 \times 2 = \dfrac{2}{2\times4} + \dfrac{2}{4\times6} + ...... + \dfrac{2}{16 \times 18} + \dfrac{2}{18 \times 20}$

$A: 2 = \dfrac{1}{2} - \dfrac{1}{4} + \dfrac{1}{4} - \dfrac{1}{6} + ..... + \dfrac{1}{16} - \dfrac{1}{18} + \dfrac{1}{18} - \dfrac{1}{20}$

$A : 2 = \dfrac{1}{2} - \dfrac{1}{20}$

$A : 2 = \dfrac{9}{20}$

$A = \dfrac{9.2}{20}$

$A = \dfrac{9}{10}$.