Standard equation of ellipse and auxiliary circleHard

Infinite Sum of Ellipse Areas

Let ${E_1}:\frac{{{x^2}}}{9} + \frac{{{y^2}}}{4} = 1$ be an ellipse. Ellipses E_i's are constructed such that their centres and eccentricities are same as that of E₁, and the length of minor axis of E_i is the length of major axis of E_i+1(i ≥ 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 ……

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