If the radii of the red circle and the blue circle as shown above are 1 and 4 respectively, find the sum of the reciprocals of the radii of the seven green circles.

The answer can be expressed as \(\dfrac{a}{b}\) where \(a\) and \(b\) are coprime positive integers. Find \(a+b\).

**Note**: All circles that seem to touch with each other and/or the line are actually tangent with them. For example, the red circle, the blue circle, and the largest green circle are tangent to each other and to the line.

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