$A = \dfrac{1}{1.2} + \dfrac{2}{2.4} + \dfrac{3}{4.7}+...+\dfrac{19}{172.191}+\dfrac{20}{191.211} $
$=\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{4}+...+\dfrac{1}{172}-\dfrac{1}{191}+\dfrac{1}{191}-\dfrac{1}{211} $
$ = 1 - \dfrac{1}{211} $
$=\dfrac{210}{211} $