$A$ $=$ $\frac{1}{2 × 3}$ + $\frac{1}{3 × 4}$ + $\frac{1}{4 × 5}$ + $\frac{1}{5 × 6}$ + $\frac{1}{6 × 7}$ + $\frac{1}{7 × 8}$
$A = \frac{1}{2} - \frac{1}{ 3} + \frac{1}{ 3} - \frac{1}{ 4} + \frac{1}{ 4} - \frac{1}{5} + \frac{1}{5} - \frac{1}{6} + \frac{1}{6} - \frac{1}{7} + \frac{1}{7} - \frac{1}{ 8}$
$A = \frac{1}{ 2} - \frac{1}{ 8} = \frac{3}{8}$