$A = \frac{1}{1.2} + \frac{1}{2.3} + .... + \frac{1}{99.100}$
$= 1 - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} +......+ \frac{1}{99} - \frac{1}{100}$
$= 1 - \frac{1}{100} = \frac{99}{100}$
$B = \frac{1}{20} + \frac{1}{30} + ...... + \frac{1}{110} + \frac{1}{132}$
$= \frac{1}{4.5} + \frac{1}{5.6} + ...... + \frac{1}{10.11} + \frac{1}{11.12}$
$= \frac{1}{4} - \frac{1}{5} + \frac{1}{5} - \frac{1}{6} +...... + \frac{1}{10} - \frac{1}{11} + \frac{1}{11} - \frac{1}{12}$
$= \frac{1}{4} - \frac{1}{12}$
$= \frac{1}{6}$