Let $p(x) \in \mathbb{Q}[x]$ be a non-constant rational polynomial with positive leading
coefficient. Is it true that \[A=\{ p(n)+1/n : n \in \mathbb{N}\}\] is strongly complete,
in the sense that, for any finite set $B$,
\[\left\{\sum_{a \in X} a : X \subseteq A \setminus B, X \textrm{ is finite}\right\}\]
contains all sufficiently large integers?
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