\(A=\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}.....\frac{2015^2}{2014.2016}=\frac{\left(2.3.4......2015\right)}{\left(1.2.3......2014\right)}.\frac{\left(2.3.4.....2015\right)}{\left(3.4.5......2016\right)}=\frac{2015}{1}.\frac{2}{2016}=\frac{2015}{1008}\)