Consider $0<\lambda<1$, and let $A$ be a multiset of positive integers. Let $A_n={a\in A: a\leq n}$. Assume that for every $n\in\mathbb{N}$, the set $A_n$ contains at most $n\lambda$ numbers. Show that there are infinitely many $n\in \mathbb{N}$ for which the sum of the elements in $A_n$ is at most $\frac{n(n+1)}{2}\lambda$. (A multiset is a set-like collection of elements in which order is ignored, but repetition of elements is allowed and multiplicity of elements is significant. For example, multisets ${1, 2, 3}$ and ${2, 1, 3}$ are equivalent, but ${1, 1, 2, 3}$ and ${1, 2, 3}$ differ.)