  Define the $k$-th Radon number $r_k$ of a convexity space as the smallest
number (if it exists) for which any set of $r_k$ points can be partitioned into
$k$ parts whose convex hulls intersect. Combining the recent abstract
fractional Helly theorem of Holmsen and Lee with earlier methods of Bukh, we
prove that $r_k$ grows linearly, i.e., $r_k\le c(r_2)\cdot k$.
