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Putnam
2016 Putnam
A2
Putnam 2016 A2
Putnam 2016 A2
Source:
December 4, 2016
Putnam
Putnam 2016
Problem Statement
Given a positive integer
n
,
n,
n
,
let
M
(
n
)
M(n)
M
(
n
)
be the largest integer
m
m
m
such that
(
m
n
−
1
)
>
(
m
−
1
n
)
.
\binom{m}{n-1}>\binom{m-1}{n}.
(
n
−
1
m
)
>
(
n
m
−
1
)
.
Evaluate
lim
n
→
∞
M
(
n
)
n
.
\lim_{n\to\infty}\frac{M(n)}{n}.
n
→
∞
lim
n
M
(
n
)
.
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