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Putnam
1994 Putnam
1
Putnam 1994 A1
Putnam 1994 A1
Source:
July 12, 2014
Putnam
inequalities
limit
college contests
Problem Statement
Suppose that a sequence
{
a
n
}
n
≥
1
\{a_n\}_{n\ge 1}
{
a
n
}
n
≥
1
satisfies
0
<
a
n
≤
a
2
n
+
a
2
n
+
1
0 < a_n \le a_{2n} + a_{2n+1}
0
<
a
n
≤
a
2
n
+
a
2
n
+
1
for all
n
∈
N
n\in \mathbb{N}
n
∈
N
. Prove that the series
∑
n
=
1
∞
a
n
\sum_{n=1}^{\infty} a_n
∑
n
=
1
∞
a
n
diverges.
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