Cho tổng B = 8/5.9 + 8/9.13 + 8/13.17 + . . . + 8/97.101 . So sánh B với 3/5 .

\(B = 2.\left( {\frac{4}{{5.9}} + \frac{4}{{9.13}} + \frac{4}{{13.17}} + ... + \frac{4}{{97.101}}} \right) = 2.\left( {\frac{1}{5} - \frac{1}{9} + \frac{1}{9} - \frac{1}{{13}} + ... + \frac{1}{{97}} - \frac{1}{{101}}} \right)\)

\( = 2.\left( {\frac{1}{5} - \frac{1}{{101}}} \right) = \frac{2}{5} - \frac{2}{{101}} < \frac{2}{5} < \frac{3}{5}\).

Vậy \(B < \frac{3}{5}\).