This problem illustrates the concept of geometric series.

The figure on the left consists of an infinite series of semicircular segments. The largest segment has a radius of R, the next one has a radius of R/2, and the radius of each subsequent segment is 1/2 that of the preceding semicircle. Show that the total length of the segments is exactly the same as the circumference of a full circle of radius R, i.e. 2pR.

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