Thực hiện phép tính một cách hợp lí:

f) \(\frac{2}{{3.7}} + \frac{2}{{7.11}} + \frac{2}{{11.15}} + ... + \frac{2}{{63.67}}.\)

i) \[\left( {1 - \frac{1}{2}} \right) \cdot \left( {1 - \frac{1}{3}} \right) \cdot \left( {1 - \frac{1}{4}} \right) \cdot \left( {1 - \frac{1}{5}} \right) \cdot \left( {1 - \frac{1}{6}} \right) \cdot \left( {1 - \frac{1}{7}} \right) \cdot \left( {1 - \frac{1}{8}} \right)\]

\[ = \left( {\frac{2}{2} - \frac{1}{2}} \right) \cdot \left( {\frac{3}{3} - \frac{1}{3}} \right) \cdot \left( {\frac{4}{4} - \frac{1}{4}} \right) \cdot \left( {\frac{5}{5} - \frac{1}{5}} \right) \cdot \left( {\frac{6}{6} - \frac{1}{6}} \right) \cdot \left( {\frac{7}{7} - \frac{1}{7}} \right) \cdot \left( {\frac{8}{8} - \frac{1}{8}} \right)\]

\[ = \frac{1}{2} \cdot \frac{2}{3} \cdot \frac{3}{4} \cdot \frac{4}{5} \cdot \frac{5}{6} \cdot \frac{6}{7} \cdot \frac{7}{8}\]\[ = \frac{1}{8}.\]