There is a question I've done before, that is
In the Harmonic series $1+\frac12+\cdots+\frac1n+\cdots$, the fraction of $1/k$ is dropped if the decimal representation contains number digits 9, then the rest of the series is convergent.
the proof is simple to me. But a long time ago(for years), I was told by someone the convergent series has a closed form. Until now I review my notes recently, I remember that takes me much efforts but got no answer, Is it true, and how?
any method can be used such as real analysis(its more like Cantor Set), special functions(I've tried generating function and derivative before)