Yesterday I posed the following problem: If $S$ is the set of positive integers whose decimal expansion does not contain a 3, does

\[ \sum_{n\in S}\frac{1}{n} \]

converge or diverge? My solution is after the break.

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Here’s a quick math problem to think about. Let $S$ be the set of positive integers which do not contain a 3 when written in decimal. Does the sum of the reciprocals of the numbers in $S$ converge or diverge? I’ll post my answer in the next day or two.