\(A=\frac{1}{11.13}+\frac{1}{13.15}+...+\frac{1}{54.55}\)
\(A=\frac{1}{2}.\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{54}-\frac{1}{55}\right)\)
\(A=\frac{1}{2}.\left(\frac{1}{11}-\frac{1}{55}\right)\)
\(A=\frac{1}{2}.\frac{4}{55}\)
\(A=\frac{2}{55}\)