
Length of LINE SEGMENT
A line segment of length 1 is divided evenly into 3 portions.
The middle section is removed.
From the remaining portions, each is again divided evenly into 3 portions and the middle part of each portions is removed.
If the process goes on for 6 times, what is the total length of the line segments, which have been removed?
*show working and explanation PLS (Nod)

This might help: Cantor set  Wikipedia, the free encyclopedia
So I guess you're trying to find $\displaystyle \displaystyle \sum_{n=0}^5 \frac{2^n}{3^{n+1}}$
This segment kinda resembles the cantor set, but there is a difference in that the segment is actually [0,1]