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Consider a series of 'n' concentric circ...

Consider a series of 'n' concentric circles `C_1, C_2, C_3, ....., C_n` with radii `r_1, r_2, r_3, ......,r_n` respectively, satisfying `r_1 > r_2 > r_3.... > r_n and r_1= 10.` The circles are such that the chord of contact of tangents from any point on `C_1` to `C_(i+1)` is a tangent to `C_(i+2) (i = 1, 2, 3,...).` Find the value of `lim_(n->oo) sum_(i=1)^n r_1,` if the angle between the tangents from any point of `C_1` to `C_2` is `pi/3.`

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