Tính nhanh: B = 4/(3x6) + 4/(6x9) + 4/(9x12) + 4/(12x15)

Hướng dẫn: 

\(B = \frac{4}{{3 \times 6}} + \frac{4}{{6 \times 9}} + \frac{4}{{9 \times 12}} + \frac{4}{{12 \times 15}}\)

\(B = 4 \times \left( {\frac{1}{{3 \times 6}} + \frac{1}{{6 \times 9}} + \frac{1}{{9 \times 12}} + \frac{1}{{12 \times 15}}} \right)\)

\(B = \frac{4}{3} \times \left( {\frac{3}{{3 \times 6}} + \frac{3}{{6 \times 9}} + \frac{3}{{9 \times 12}} + \frac{3}{{12 \times 15}}} \right)\)

\(B = \frac{4}{3} \times \left( {\frac{{6 - 3}}{{3 \times 6}} + \frac{{9 - 6}}{{6 \times 9}} + \frac{{12 - 9}}{{9 \times 12}} + \frac{{15 - 12}}{{12 \times 15}}} \right)\)

\(B = \frac{4}{3} \times \left( {\frac{1}{3} - \frac{1}{6} + \frac{1}{6} - \frac{1}{9} + \frac{1}{9} - \frac{1}{{12}} + \frac{1}{{12}} - \frac{1}{{15}}} \right)\)

\(B = \frac{4}{3} \times \left( {\frac{1}{3} - \frac{1}{{15}}} \right) = \frac{4}{3} \times \frac{4}{{15}} = \frac{{16}}{{45}}\)