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A series of concentric ellipses E1,E2, E...

A series of concentric ellipses `E_1,E_2, E_3..., E_n` are drawn such that E touches the extremities of the major axis of `E_(n-1)`, and the foci of `E_n` coincide with the extremities of minor axis of `E_(n-1)` If the eccentricity of the ellipses is independent of n, then the value of the eccentricity, is (A) `sqrt 5/3` (B) `(sqrt 5-1)/2` (C) `(sqrt 5 +1)/2` (D) `1/sqrt5`

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