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Putnam
2021 Putnam
B2
B2
Part of
2021 Putnam
Problems
(1)
Putnam 2021 B2
Source:
12/5/2021
Determine the maximum value of the sum
S
=
∑
n
=
1
∞
n
2
n
(
a
1
a
2
…
a
n
)
1
n
S=\sum_{n=1}^{\infty}\frac{n}{2^n}(a_1 a_2 \dots a_n)^{\frac{1}{n}}
S
=
n
=
1
∑
∞
2
n
n
(
a
1
a
2
…
a
n
)
n
1
over all sequences
a
1
,
a
2
,
a
3
,
…
a_1,a_2,a_3,\dots
a
1
,
a
2
,
a
3
,
…
of nonnegative real numbers satisfying
∑
k
=
1
∞
a
k
=
1.
\sum_{k=1}^{\infty}a_k=1.
k
=
1
∑
∞
a
k
=
1.
Putnam
Putnam 2021