(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let E be the set of points in [0,1) whose decimal expansion contains somewhere the block 55555. Find the measure of E.

2. Relevant equations

3. The attempt at a solution

I have a feeling that in order to find the measure of E, I should find the measure of the complement of E and then subtract it from 1. The complement of E would be the points in [0,1) containing no 5's, containing no consecutive 5's, containing 2 consecutive 5's, containing 3 consecutive 5's, containing 3 consecutive 5's, or containing 4 consecutive 5's. I'm not sure how to compute the measure of this set, however.

Any help would be greatly appreciated!

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# Homework Help: Analysis - How many numbers in the interval [0,1) contain 5 consecutive 5's?

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