Ta có
$M = \dfrac{4 + \frac{2}{1007} - \frac{4}{2015} + \frac{1}{504} - \frac{4}{2017}}{\frac{1}{288} - \frac{7}{2017} + \frac{7}{2014} - \frac{7}{2015} + 7}$
$= \dfrac{ \frac{4}{7} \left( 7 + \frac{7}{2.1007} - \frac{7}{2015} + \frac{7}{4.504} - \frac{7}{2017} \right)}{\frac{1}{288} - \frac{7}{2017} + \frac{7}{2014} - \frac{7}{2015} + 7}$
$= \dfrac{4}{7} \dfrac{7 + \frac{7}{2014} - \frac{7}{2015} + \frac{1}{288} - \frac{7}{2017}}{\frac{1}{288} - \frac{7}{2017} + \frac{7}{2014} - \frac{7}{2015} + 7}$
$= \dfrac{4}{7} . 1 = \dfrac{4}{7}$
Vậy $M = \dfrac{4}{7}$.
