Prove that the following expression is not an integer

Hint: Between integers k and 2k, there exists a prime (I know this is a wierd result that i am using.. but cos this stuff is in olympiad stuff .. u need to know this !)

Seems no one has any clue!!

Ok i will put a solution

1/2+1/3+1/4.....+1/n

let p be the largest prime less than n.

Then, p<=n<2p !!!!

This might be a long shot!

But what this comes from is that between n and 2n there is always a prime!
Search "Proof of Bertrand's postulate"

So if we assume that 2p<n

then there will be a prime between p and 2p.. so there will be a prime larger than p but smaller than n!

So we have only one denominator that is divisible by p

so this whole sum will have only one number with denominator p

This fraction cannot be removed!

Hence this sum is never an integer!!