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Putnam
1994 Putnam
1
1
Part of
1994 Putnam
Problems
(2)
Putnam 1994 A1
Source:
7/12/2014
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.
Putnam
inequalities
limit
college contests
Putnam 1994 B1
Source:
7/12/2014
Find all positive integers that are within
250
250
250
of exactly
15
15
15
perfect squares.
Putnam
college contests