Ms. Cohei wrote in an email from Japan:
"Incidentally, I wrote a program for the Harmonic Series in C language. Just for reference your information, here it is:
I was very excited with this program because it could calculate the sum total of one billion terms of the Harmonic Series !
Thank you very much. Cohei"
It's wonderful to hear from people who are really reading my books and using them with their children. It's nice to know I'm not perfect, and I'm always learning new things. This series tends to infinity, diverges, but very slowly.
In about 1350 Oresme proved this series to be divergent. The proof is based on the idea that pieces of the harmonic series are > 1/2 and the series 1/2 + 1/2 + 1/2 +... diverges, the harmonic series also diverges. See my worksheet book for the proof.