$a) \dfrac{8}{19} . \dfrac{5}{11} + \dfrac{7}{19} . \dfrac{8}{11} - \dfrac{8}{19} . \dfrac{1}{11}$
$= \dfrac{8}{19} . \dfrac{5}{11} + \dfrac{8}{19} . \dfrac{7}{11} - \dfrac{8}{19} . \dfrac{1}{11}$
$= \dfrac{8}{19} . (\dfrac{5}{11} + \dfrac{7}{11} - \dfrac{1}{11})$
$= \dfrac{8}{19} . \dfrac{11}{11}$
$= \dfrac{8}{19} . 1$
$= \dfrac{8}{19}$
$b$)
Đặt $A = 1 + \dfrac{1}{2} + \dfrac{1}{2^2} + \dfrac{1}{2^3} + ..... + \dfrac{1}{2^{100}}$
$2A = 2 + 1 + \dfrac{1}{2} + \dfrac{1}{2^2} + .... + \dfrac{1}{2^{99}}$
$2A-A= (2 + 1 + \dfrac{1}{2} + \dfrac{1}{2^2} + .... + \dfrac{1}{2^{99}})-(1 + \dfrac{1}{2} + \dfrac{1}{2^2} + \dfrac{1}{2^3} + ..... + \dfrac{1}{2^{100}})$
$A = 2 - \dfrac{1}{2^{100}}$
$A = \dfrac{2^{101}-1}{2^{100}}$
