$1$. $A = \dfrac{1}{30} + \dfrac{1}{42} + \dfrac{1}{56} + \dfrac{1}{72} + \dfrac{1}{90} + \dfrac{1}{110} + \dfrac{1}{132}$
$A = \dfrac{1}{5.6} + \dfrac{1}{6.7} + \dfrac{1}{7.8} + \dfrac{1}{8.9} + \dfrac{1}{9.10} + \dfrac{1}{10.11} + \dfrac{1}{11.12}$
$A = \dfrac{1}{5} - \dfrac{1}{6} + \dfrac{1}{6} - \dfrac{1}{7} + \dfrac{1}{7} - \dfrac{1}{8} + \dfrac{1}{8} - \dfrac{1}{9} + \dfrac{1}{9} - \dfrac{1}{10} + \dfrac{1}{10} - \dfrac{1}{11} + \dfrac{1}{11} - \dfrac{1}{12}$
$A = \dfrac{1}{5} - \dfrac{1}{12}$
$A = \dfrac{7}{60}$
$2$. $S = 3 + \dfrac{3}{2} + \dfrac{3}{2^2} + \dfrac{3}{2^3} + .... + \dfrac{3}{2^9}$
$2S = 6 + 3 + \dfrac{3}{2} + \dfrac{3^2} + ... + \dfrac{3}{2^8}$
$2S - S =( 6 + 3 + \dfrac{3}{2} + \dfrac{3^2} + ... + \dfrac{3}{2^8}) - (3 + \dfrac{3}{2} + \dfrac{3}{2^2} + \dfrac{3}{2^3} + .... + \dfrac{3}{2^9})$
$S = 6 - \dfrac{3}{2^9}$
$S = 6 - \dfrac{3}{512}$
$S = \dfrac{3069}{512}$
