\(A=\dfrac{5}{2\cdot9}+\dfrac{5}{9\cdot16}+...+\dfrac{5}{252\cdot259}\)
\(=\dfrac{5}{7}\left(\dfrac{1}{2}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{16}+...+\dfrac{1}{252}-\dfrac{1}{259}\right)\)
\(=\dfrac{5}{7}\cdot\dfrac{257}{2\cdot259}\)
\(=\dfrac{1285}{3626}\)