If A ⊂ ℕ is a finite set of integers all of whose subset sums are distinct then ∑ n ∈ A, 1/n < 2. Proved by Ryavec.

If A ⊂ ℕ is a finite set of integers all of whose subset sums are distinct then ∑ n ∈ A, 1/n^s < 1/(1 - 2^(-s)), for any s > 0. Proved by Hanson, Steele, and Stenger [HSS77].

We exclude here the case s = 0, because in the informal formulation then the right hand side is to be interpreted as ∞, while the left hand side counts the elements in A.