Question: This problem shows how you can create a fractal called a Cantor Set. Take a line segment of length 1, divide it into three equal pieces and remove the middle piece. We are left with two smaller line segments. At the second stage, remove the middle third of each of the two segments. We now have four smaller line segments left. At the third stage, remove the middle third of each of the remaining segments. Continue in this manner.
(a) Draw a picture that illustrates this process.
(b) Find a series that gives the total length of the pieces we have removed after the nth stage.
(c) If we continue the process indefinitely, what is the total length of the pieces that we remove?