Exercise 21, § 1

Show that for $m \geq 1$ and $n \geq 1$ the rational number $\sum_{k=n}^{n+m} k^{-1}$ is never an integer (if $2^q$ is the largest power of 2 which divides at least one of the numbers $n, n+1, \ldots, n+m$, then it divides only one of these numbers).