A=1/8 +1/24 +1/48 +1/80 +1/120

$\displaystyle \begin{array}{{>{\displaystyle}l}} A=\frac{1}{8} +\frac{1}{24} +\frac{1}{48} +\frac{1}{80} +\frac{1}{120}\\ \ \ =\frac{1}{2.4} +\frac{1}{4.6} +\frac{1}{6.8} +\frac{1}{8.10} +\frac{1}{10.12} \end{array}$ $\displaystyle \begin{array}{{>{\displaystyle}l}} \Rightarrow 2A=\frac{2}{2.4} +\frac{2}{4.6} +\frac{2}{6.8} +\frac{2}{8.10} +\frac{2}{10.12}\\ \ \ \ \ \ \ \ \ \ \ \ =\frac{1}{2} -\frac{1}{4} +\frac{1}{4} -\frac{1}{6} +\frac{1}{6} -\frac{1}{8} +\frac{1}{8} -\frac{1}{10} +\frac{1}{10} -\frac{1}{12}\\ \ \ \ \ \ \ \ \ \ \ \ =\frac{1}{2} -\frac{1}{12} =\frac{5}{12} \end{array}$ $\displaystyle \Rightarrow A=\frac{5}{24}$