The Cantor set (Georg Cantor, 1845-1918) is a subset of the unit interval [0, 1]. To construct the Cantor set, first remove the middle third of the interval, leaving two line segments. For the second step, remove the middle third of each of the two remaining segments, leaving four line segments. Continue this procedure indefinitely, as shown in the figure. The Cantor set consists of all numbers in the unit interval [0, 1] that still remain.

(a) Find the total length of all the line segments that are removed.
(b) Write down three numbers that are in the Cantor set.

(c) Let C_n denote the total length of the remaining line segments after steps. Find

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