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Consider ellipses E:k =kx^2+k^2y^2=1, k=...

Consider ellipses `E:_k =kx^2+k^2y^2=1, k=1, 2..... 20`. Let `C_2` be the circle which touches the four chords joining the end points (one on minor axis and another on major axis) of the ellipse `E_k`. If `r_k` is the radius of the circle `C_k`, then the value of `sum_(k=1)^(20) 1/(r_k)^2` is

A

2870

B

3080

C

3320

D

3210

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