What is the set elements for $K_1$ and $K_2$ according to given definition

[tallmonkey]

As the title says, how should I construct K_n. I am confused because am I just supposed to add the Geometric series I get?

 

[Dr.Peterson]

View attachment 31938
As the title says, how should I construct K_n. I am confused because am I just supposed to add the Geometric series I get?

You could describe this set geometrically; but you haven't shown what you are actually told to do with the set, so I have no idea what you are supposed to do (e.g. find the measure of the set, or whatever). Please show the entire problem.

What geometric series do you have? I don't see one here; but that would give you a number, not a set.

Now, if the title is supposed to be what they asked you to do (paraphrased), it would appear to be asking for an explicit description of the first two instances of such a set, probably as a union of intervals. Do you see that K₁ consists of all numbers that are written in base 5 as 0.0..., 0.1..., 0.3..., or 0.4...? What would that look like on a number line?