Harmonic Sum

1. Jun 15, 2006

Dragonfall

How do I show that $$\sum_1^n\frac{1}{k}$$ is not an integer for n>1? I tried bounding them between two integrals but that doesn't cut it. I know that $$\sum_1^n\frac{1}{k}=\frac{(n-1)!+n(n-2)!+n(n-1)(n-3)!+...+n!}{n!}$$ but I can't get a contradiction.

2. Jun 15, 2006

StatusX

Last edited by a moderator: Apr 22, 2017