\(A=\dfrac{1}{2}\left(\dfrac{4}{11\cdot15}+\dfrac{4}{15\cdot19}+...+\dfrac{4}{51\cdot55}\right)\)
=1/2(1/11-1/15+1/15-1/19+...+1/51-1/55)
=1/2*4/55=2/55
B=-5/3*4/3*11/2=-110/9
\(A\cdot B=\dfrac{2}{55}\cdot\dfrac{-110}{9}=\dfrac{-2\cdot2}{9}=\dfrac{-4}{9}\)