Prove that $1 + \frac{1}{2} + \frac{1}{3} + ... + \frac{1}{n}$ is not an integer 
Possible Duplicate:
Is there an elementary proof that $∑_{k=1}^n 1/k$ is never an integer? 

Hello,

Prove that $1 + \frac{1}{2} + \frac{1}{3} + ... + \frac{1}{n}$ is not an integer.

I tried to prove by induction on $n$, but I was stuck :(
Assume $1 + \frac{1}{2} + \frac{1}{3} + ... + \frac{1}{n} = \frac{a}{b}$ for some integers $a, b$ and $a \neq b \text{and} b \neq 0$
Then $ 1 + \frac{1}{2} + \frac{1}{3} + ... + \frac{1}{n + 1} = \frac{a}{b} + \frac{1}{n + 1}$
Then how can I prove that this expression is not integer? A hint would be greatly appreciated.  
Thanks,
Chan

Hint: look at the largest power of 2 less than $n$. Can it get canceled out from the denominator?
