$A = \frac{1}{1.2} + \frac{1}{2.3} + .... + \frac{1}{99.100}$

    $= 1 - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} +......+ \frac{1}{99} - \frac{1}{100}$

    $= 1 - \frac{1}{100} = \frac{99}{100}$

$B = \frac{1}{20} + \frac{1}{30} + ...... + \frac{1}{110} + \frac{1}{132}$

     $= \frac{1}{4.5} + \frac{1}{5.6} + ...... + \frac{1}{10.11} + \frac{1}{11.12}$

     $= \frac{1}{4} - \frac{1}{5} + \frac{1}{5} -  \frac{1}{6} +...... + \frac{1}{10} - \frac{1}{11} + \frac{1}{11} - \frac{1}{12}$

     $= \frac{1}{4} - \frac{1}{12}$

     $= \frac{1}{6}$

a)$A=\dfrac{1}{1.2}+$ $\dfrac{1}{2.3}+$ $\dfrac{1}{3.4}+$ $\dfrac{1}{4.5}+...+$ $\dfrac{1}{99.100}$ 

$A=1-\dfrac{1}{2}+$ $\dfrac{1}{2}-$ $\dfrac{1}{3}+$ $\dfrac{1}{3}-$ $\dfrac{1}{4}+$ $\dfrac{1}{4}-$ $\dfrac{1}{5}+...+$ $\dfrac{1}{99}-$ $\dfrac{1}{100}$

$A=1-\dfrac{1}{100}$

$A=\dfrac{99}{100}$

b) Mình không ghi lại đề nữa nhé!

$B=\dfrac{1}{4.5}+$ $\dfrac{1}{5.6}+$ $\dfrac{1}{6.7}+...+$ $\dfrac{1}{11.12}$

$B=\dfrac{1}{4}-$ $\dfrac{1}{5}+$ $\dfrac{1}{5}-$ $\dfrac{1}{6}+...+$ $\dfrac{1}{11}-$ $\dfrac{1}{12}$

$B=\dfrac{1}{4}-$ $\dfrac{1}{12}$

$B=\dfrac{2}{12}=$ $\dfrac{1}{6}$