a) $A=\dfrac{1}{4×5}+$ $\dfrac{1}{5×6}+$ $\dfrac{1}{6×7}+$ $\dfrac{1}{6×7}$
$A=\dfrac{1}{4}-$ `1/5+1/5-1/6+1/6-1/7+1/7-1/8`
$A=$`1/4-1/8`
$A=$`2/8-1/8`
$A=$`1/8`
b) $S=\dfrac{1}{1×3}+$ $\dfrac{1}{3×5}+$ $\dfrac{1}{5×7}+$ $\dfrac{1}{7×9}$
$S=\dfrac{1}{2}×$$(\dfrac{2}{1×3}$ $+$ $\dfrac{2}{3×5}$ $+$ $\dfrac{2}{5×7}$$+$$\dfrac{2}{7×9})$
$S=\dfrac{1}{2}×$`(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9)`
$S=\dfrac{1}{2}×$`(1-1/9)`
$S=\dfrac{1}{2}×$`8/9`
$S=$`4/9`