Tính giá trị của biểu thức một cách hợp lí: \(A = \frac{3}{5} + \frac{3}{{20}} + \frac{3}{{44}} + \frac{3}{{77}}\).

Ta có \(A = \frac{3}{5} + \frac{3}{{20}} + \frac{3}{{44}} + \frac{3}{{77}}\)\( = 2\left( {\frac{3}{{10}} + \frac{3}{{40}} + \frac{3}{{88}} + \frac{3}{{154}}} \right)\)

\( = 2\left( {\frac{3}{{2.5}} + \frac{3}{{5.8}} + \frac{3}{{8.11}} + \frac{3}{{11.14}}} \right)\)

\( = 2\left[ {\left( {\frac{1}{2} - \frac{1}{5}} \right) + \left( {\frac{1}{5} - \frac{1}{8}} \right) + \left( {\frac{1}{8} - \frac{1}{{11}}} \right) + \left( {\frac{1}{{11}} - \frac{1}{{14}}} \right)} \right]\)

\( = 2\left( {\frac{1}{2} - \frac{1}{5} + \frac{1}{5} - \frac{1}{8} + \frac{1}{8} - \frac{1}{{11}} + \frac{1}{{11}} - \frac{1}{{14}}} \right)\)

\( = 2\left( {\frac{1}{2} - \frac{1}{{14}}} \right) = 2.\frac{3}{7} = \frac{6}{7}\).

Vậy \(A = \frac{3}{5} + \frac{3}{{20}} + \frac{3}{{44}} + \frac{3}{{77}} = \frac{6}{7}\).