Let E_1: x^2/9+y^2/4=1 be an ellipse. Ellipses E_i 's are constructed such that their centres and eccentricities are same as that of E_1, and the…

Let $\displaystyle \mathrm{E}_1: \frac{x^2}{9}+\frac{y^2}{4}=1$ be an ellipse. Ellipses $\displaystyle \mathrm{E}_{\mathrm{i}}$ 's are constructed such that their centres and eccentricities are same as that of $\displaystyle E_1$, and the length of minor axis of $\displaystyle \mathrm{E}_{\mathrm{i}}$ is the length of major axis of $\displaystyle E_{i+1}(i \geq 1)$. If $\displaystyle A_i$ is the area of the ellipse $\displaystyle E_i$, then $\displaystyle \frac{5}{\pi}\left(\sum_{i=1}^{\infty} A_i\right)$, is equal to $\displaystyle \_\_\_\_$.