"Given (rn), rn E (0,1), define a generalized Cantor set E by removing the middle r1 fraction of an interval, then remove the middle r2 fraction of the remaining 2 intervals, etc. Start with [0,1]. Take rn=1/5n. Then the material removed at the n-th stage has length < 1/5n, so the total length removed is < 1/5 + 1/52 + 1/53 +... = 1/4 Thus the length of E is >3/4. " ========================= I don't understand why the material removed at the n-th stage has length < 1/5n. How can we derive this? At the n-th stage, we are removing 2n-1 pieces, so don't we have to multiply that by 2n-1? I sat down and thought about this for half an hour, but I still can't figure it out. I hope someone can explain this! Thank you!