Tính giá trị biểu thức:

$A = \frac{2}{{4.9}} + \frac{2}{{9.14}} + \frac{2}{{14.19}} + ... + \frac{2}{{44.49}}$

$\begin{array}{l}A = \frac{2}{{4.9}} + \frac{2}{{9.14}} + \frac{2}{{14.19}} + ... + \frac{2}{{44.49}}\\ = \frac{2}{5}\left( {\frac{5}{{4.9}} + \frac{5}{{9.14}} + \frac{5}{{14.19}} + ... + \frac{5}{{44.49}}} \right)\end{array}$

= $\frac{2}{5}.\left( {\frac{1}{4} - \frac{1}{9} + \frac{1}{9} - \frac{1}{{14}} + \frac{1}{{14}} - \frac{1}{{19}} + ... + \frac{1}{{44}} - \frac{1}{{49}}} \right)$

= $\frac{2}{5}.\left( {\frac{1}{4} - \frac{1}{{49}}} \right) = \frac{2}{5}.\frac{{45}}{{196}} = \frac{9}{{98}}$