$C(n)$ is defined as the set that remains after removing from $[0, 1]$ an open interval of length 1/n centered at 1/2, then an open interval of length $1/n^2$ from the center of each of the two remaining intervals, then open intervals of length $1/n^3$ from the centers of each of the remaining $4=2^2$ intervals, and so on.
How would I show that the measure of $C(n)$ is $\frac{n-3}{n-2}$?
Any hints greatly appreciated: By drawing out examples for small n, I would think that the measure is 0 since we are continuously removing open intervals and keeping the endpoints. I also see that C(3) = 0 since C(3) is the Cantor set.