Define the collections {E_1, E_2, E_3, ... } of ellipses and {R_1, R_2, R_3, ... } of rectangles as follows:
$$E_1: \frac{x^2}{9} + \frac{y^2}{4} = 1$$;
$$R_1$$: rectangle of largest area, with sides parallel to the axes, inscribed in $$E_1$$;
$$E_n$$: ellipse $$\frac{x^2}{a_n^2} + \frac{y^2}{b_n^2} = 1$$ of largest area inscribed in $$R_{n - 1}, n > 1$$
$$R_n$$: rectangle of largest area, with sides parallel to the axes, inscribed in $$E_n, n > 1$$
Then which of the following options is/are correct?