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2022 HMIC
3
Trivial by direct computation
Trivial by direct computation
Source: HMIC 2022/3
April 8, 2022
algebra
number theory
Problem Statement
For a nonnegative integer
n
n
n
, let
s
(
n
)
s(n)
s
(
n
)
be the sum of the digits of the binary representation of
n
n
n
. Prove that
∑
n
=
1
2
2022
−
1
(
−
1
)
s
(
n
)
n
+
2022
>
0.
\sum_{n=1}^{2^{2022}-1} \frac{(-1)^{s(n)}}{n+2022}>0.
n
=
1
∑
2
2022
−
1
n
+
2022
(
−
1
)
s
(
n
)
>
0.
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