  A $k$-sum of a set $A\subseteq \mathbb{Z}$ is an integer that may be
expressed as a sum of $k$ distinct elements of $A$. How large can the ratio of
the number of $(k+1)$-sums to the number of $k$-sums be? Writing $k\wedge A$
for the set of $k$-sums of $A$ we prove that \[ \frac{|(k+1)\wedge A|}{|k\wedge
A|}\, \le \, \frac{|A|-k}{k+1} \] whenever $|A|\ge (k^{2}+7k)/2$. The
inequality is tight -- the above ratio being attained when $A$ is a geometric
progression. This answers a question of Ruzsa.
