\(A=\dfrac{1}{7}\left(\dfrac{555}{777}+\dfrac{4444}{12221}+\dfrac{33333}{244442}+\dfrac{11}{30}+\dfrac{13}{30}\right)\)
\(=\dfrac{1}{7}\left(\dfrac{5}{7}+\dfrac{4}{11}+\dfrac{3}{22}+\dfrac{23}{30}\right)\\ =\dfrac{1}{7}\left(\dfrac{5}{7}+\dfrac{1}{2}+\dfrac{23}{30}\right)\\ =\dfrac{1}{7}\cdot\dfrac{208}{105}\\ =\dfrac{208}{735}\)