We know that $\sum^n_{k=1}\frac1k$ diverges. But if I were to pick a digit $p$ so that $p$ is an integer between $0$ and $9$ inclusive, and then I removed all terms in the sum $\sum^n_{k=1}\frac1k$ containing the digit $p$, what does the sum converge to, if it converges at all?
After a few hours considering this problem, I have decided that the problem is beyond me and I need help.
