$A = \frac{1}{2.3} + \frac{2}{3.5} + \frac{3}{5.8} + \frac{4}{8.12} + \frac{5}{12.17} + \frac{6}{17.23} + \frac{7}{23.30}$
$A = \frac{1}{2} - \frac{1}{3} + \frac{1}{3} - \frac{1}{5} + \frac{1}{5} - \frac{1}{8} + \frac{1}{8} - \frac{1}{12} + \frac{1}{12} - \frac{1}{17} + \frac{1}{17} - \frac{1}{23} + \frac{1}{23} - \frac{1}{30}$
$A = \frac{1}{2} - \frac{1}{30}$
$A = \frac{15}{30} - \frac{1}{30}$
$A = \frac{14}{30} = \frac{7}{15}$
