Folner sequences and sum-free sets

Erdos showed that every set of n positive integers contains a subset of size at least n/(k + 1) containing no solutions to x(1) + ... + x(k) = y. We prove that the constant 1/(k + 1) here is best possible by showing that is (F-m) is a Multiplicative Folner sequence in N, then F-m has no k-sum-free subset of size greater than (1/(k + 1) + 0(1))|F-m|.