Convergence of Harmonic Series with Omitted 9s in Denominator

[Nobody1111]

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

 

[NateTG]

Hmm, you could search for similar threads on this site. Nah, that would make too much sense.

https://www.physicsforums.com/showthread.php?t=17344&highlight=harmonic+series

 

[matt grime]

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?