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Putnam
1981 Putnam
B5
Putnam 1981 B5
Putnam 1981 B5
Source: Putnam 1981
March 31, 2022
Putnam
Summation
Binary
Problem Statement
Let
B
(
n
)
B(n)
B
(
n
)
be the number of ones in the base two expression for the positive integer
n
.
n.
n
.
Determine whether
exp
(
∑
n
=
1
∞
B
(
n
)
n
(
n
+
1
)
)
\exp \left( \sum_{n=1}^{\infty} \frac{ B(n)}{n(n+1)} \right)
exp
(
n
=
1
∑
∞
n
(
n
+
1
)
B
(
n
)
)
is a rational number.
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