Convergence of Harmonic Series with Omitted 9s in Denominator

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The discussion centers on the convergence of a modified harmonic series where terms with a denominator containing the digit '9' are omitted. The series in question is represented as 1 + 1/2 + 1/3 + 1/4 + ... excluding terms like 1/9, 1/19, and others. Participants confirm that this series converges, providing a proof for its convergence. The conversation also references previous discussions and proofs related to this topic.

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Nobody1111
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In the harmonic series 1+1/2+1/3+1/4+... we omit expressions which contain digit 9 in denominator (so we omit e.g. 1/9, 1/19, 1/94, 1/893, 1/6743090 etc.). Proof that such series is convergent.

Have You got any idea how to solve this problem?

Thanks a lot for help
 
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I'd forgotten I'd proved this result... I didn't check the dates, but is it exactly one year on? Same course, same homework different year?
 

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