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Giải thích các bước giải:

$B = \dfrac{36}{1.3.5} + \dfrac{36}{3.5.7} + \dfrac{36}{5.7.9} + ... + \dfrac{36}{25.27.29}$   

$\to B = 9.\left ( \dfrac{4}{1.3.5} + \dfrac{4}{3.5.7} + \dfrac{4}{5.7.9} + ... + \dfrac{4}{25.27.29} \right )$

$\to B = 9.\left [ \dfrac{1}{3}.\left ( \dfrac{4}{1.5} \right ) + \dfrac{1}{5}.\left ( \dfrac{4}{3.7} \right ) + \dfrac{1}{7}.\left ( \dfrac{4}{5.9} \right ) + ... + \dfrac{1}{27}.\left ( \dfrac{4}{25.29} \right ) \right ]$

$\to B = 9.\left [ \dfrac{1}{3}.\left ( 1 - \dfrac{1}{5} \right ) + \dfrac{1}{5}.\left ( \dfrac{1}{3} - \dfrac{1}{7} \right ) + \dfrac{1}{7}.\left ( \dfrac{1}{5} - \dfrac{1}{9} \right ) + ... + \dfrac{1}{27}.\left ( \dfrac{1}{25} - \dfrac{1}{29} \right ) \right ]$

$\to B = 9.\left ( \dfrac{1}{1.3} - \dfrac{1}{3.5} + \dfrac{1}{3.5} - \dfrac{1}{5.7} + \dfrac{1}{5.7} - \dfrac{1}{7.9} + ... + \dfrac{1}{25.27} - \dfrac{1}{27.29} \right )$

$\to B = 9.\left ( \dfrac{1}{1.3}  - \dfrac{1}{27.29} \right )$

$\to B = 3 - \dfrac{9}{783}$

$\to B = \dfrac{260}{87}$