Tính giá trị của biểu thức \(B = \frac{4}{{1.4}} + \frac{4}{{4.7}} + \frac{4}{{7.10}} + .... + \frac{4}{{94.97}} + \frac{4}{{97.100}}\).

Ta có: \(B = \frac{4}{{1.4}} + \frac{4}{{4.7}} + \frac{4}{{7.10}} + .... + \frac{4}{{94.97}} + \frac{4}{{97.100}}\)

\(B = 4\left( {\frac{1}{{1.4}} + \frac{1}{{4.7}} + \frac{1}{{7.10}} + .... + \frac{1}{{94.97}} + \frac{1}{{97.100}}} \right)\)

\(B = \frac{4}{3}\left( {\frac{3}{{1.4}} + \frac{3}{{4.7}} + \frac{3}{{7.10}} + .... + \frac{3}{{94.97}} + \frac{3}{{97.100}}} \right)\)

\(B = \frac{4}{3}\left( {1 - \frac{1}{4} + \frac{1}{4} - \frac{1}{7} + \frac{1}{7} - \frac{1}{{10}} + .... + \frac{1}{{94}} - \frac{1}{{97}} + \frac{1}{{97}} - \frac{1}{{100}}} \right)\)

\(B = \frac{4}{3}\left( {1 - \frac{1}{{100}}} \right)\)

\(B = \frac{4}{3}.\frac{{99}}{{100}}\)

\(B = \frac{{33}}{{25}}.\)

Vậy \(B = \frac{{33}}{{25}}.\)