Let ${{\rm{E}}_1}:\frac{{{x^2}}}{9} + \frac{{{y^2}}}{4} = 1$ be an ellipse. Ellipses ${{\rm{E}}_1}$'s are constructed such that their centres and eccentricities are same as that of ${{\rm{E}}_1}$, and the length of minor axis of ${E_i}$ is the length of major axis of ${E_{i + 1}}(i \ge 1)$ . If ${A_i}$ is the area of the ellipse ${E_i}$, then $\frac{5}{\pi }\left( {\sum\limits_{i = 1}^\infty {{A_i}} } \right)$, is equal to _____ .