Solving Summation Problem: Show f(n) is Not an Integer

[VeeEight]

Homework Statement

Let f(n) = 1/2 + 1/3 + ... + 1/n
Show that f(n) is not an integer for any positive integer n

The Attempt at a Solution

I think that rearraning/breaking down the statement might be easier than applying a theorem since it seems like a simpler problem. Simply arranging the terms got pretty messy so I think the best method is to try to find an integer C such that C x f(n) is not a integer for any value of n. I tried different ways of computing such an integer C, such as taking C to be (n-1)! or something similar for that the summation will give a bunch of integers plus one term that is not an integer but I failed to find such a value. Hopefully someone can help me out over here. Thanks.

 

[stunner5000pt]

I'm a little rusty on this stuff but couldn't we solve this using induction?

 

[asleight]

The funny thing is $$f(1)=1/1$$ and $$1$$ is an integer. But, aside from that, IDK.