\(\Rightarrow A=\frac{1}{2}.\left(\frac{2}{3.5}+\frac{2}{5.7}+......+\frac{2}{13.15}\right)\)
\(\Rightarrow A=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+............+\frac{1}{13}-\frac{1}{15}\right)\)
\(\Rightarrow A=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{15}\right)\)
\(\Rightarrow A=\frac{1}{2}.\frac{4}{15}\)
\(\Rightarrow A=\frac{2}{15}\)