MathDB
SEEMOUS 2022 Problem 4

Source: SEEMOUS 2022

May 29, 2022
SubsetsConvergencebinary representationreal analysis

Problem Statement

Let F\mathcal{F} be the family of all nonempty finite subsets of N∪{0}.\mathbb{N} \cup \{0\}. Find all real numbers aa for which the series ∑A∈F1∑k∈Aak\sum_{A \in \mathcal{F}} \frac{1}{\sum_{k \in A}a^k} is convergent.
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