$M = \dfrac{1}{2} + \dfrac{1}{2.3} + \dfrac{1}{3.4} + \dfrac{1}{4.5} + \dfrac{1}{5.6} + \dfrac{1}{6.7}$
$=\dfrac{1}{2} + \dfrac{1}{2} - \dfrac{1}{3} + \dfrac{1}{3} - \dfrac{1}{4} + ... + \dfrac{1}{6} - \dfrac{1}{7}$
$=2.\dfrac{1}{2} - \dfrac{1}{7}$
$= 1 - \dfrac{1}{7}$
$=\dfrac{6}{7}$