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Help this is hard

 

Let S be the set of all real numbers of the form

a1/3 + a2/3^2 + a3/3^3 + ....
where a_i \in {0, 1, 2} for all i.

 

(a) Is the number 1/7 in the set S?

(b) Is the number 1/4 in the set S?

 Feb 11, 2023
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(a) No, 1/7 is not in the set S.

(b) Yes, 1/4 is in the set S. The number 1/4 can be expressed as 1/3^2 + 1/3^4 + 1/3^5 + ..., which is a series that converges to 1/4.

 Feb 11, 2023

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