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SEEMOUS
2022 SEEMOUS
4
4
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(1)
SEEMOUS 2022 Problem 4
Source: SEEMOUS 2022
5/29/2022
Let
F
\mathcal{F}
F
be the family of all nonempty finite subsets of
N
∪
{
0
}
.
\mathbb{N} \cup \{0\}.
N
∪
{
0
}
.
Find all real numbers
a
a
a
for which the series
∑
A
∈
F
1
∑
k
∈
A
a
k
\sum_{A \in \mathcal{F}} \frac{1}{\sum_{k \in A}a^k}
A
∈
F
∑
∑
k
∈
A
a
k
1
is convergent.
Subsets
Convergence
binary representation
real analysis