$\dfrac1 {1.2} + \dfrac1 {2.3} + ... + \dfrac1 {49.50}$
$\dfrac{2-1} {1.2} + \dfrac{3-2} {2.3} + ... + \dfrac{50-49} {49.50}$
$=\dfrac1 {1}-\dfrac1 {2} + \dfrac1 {2} -\dfrac1 {3}+ ... + \dfrac1 {49}-\dfrac1 {50}$
$=\dfrac1 {1}-\dfrac1 {50}$
$=\dfrac{49} {50}$