Math Help Forum - View Single Post

shawsend · #15 October 12th, 2008, 09:48 AM

Quote:

Originally Posted by ThePerfectHacker

1) Let $n\geq 2$ prove that $1 - \frac{1}{2}+\frac{1}{3} - ... \pm \frac{1}{n}$ is not an integer.

I'm confussed since $\sum_{k=1}^{n}\frac{(-1)^{n+1}}{k}<1$

However $H_n=\sum_{k=1}^{n}\frac{1}{k}\to\infty$ and my understanding is that $H_n$ is never an integer for $n>1$ . This one would seem to be more interesting to prove.

[edit] I think that's what Susan did. Never mind but perhaps we should make it explicit that's what's going on.