(Solved): (Crazy Iguana) The outer circle is of radius 2 , and the next circles are of radius 1 each, then th ...

(Crazy Iguana) The outer circle is of radius 2 , and the next circles are of radius 1 each, then the next set-in are of radius $\frac{1}{2}$, and so on. The blue circles are shaded because they are the area, and the white regions are void. Though I have drawn only six circles for "Crazy Iguana", imagine there are infinitely many circles constructed in the same way. Notice that these circles are tangent to the outer circle. What is the area of the infinitely constructed shape?