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Putnam
1997 Putnam
1
Putnam 1997 B1
Putnam 1997 B1
Source:
May 30, 2014
Putnam
college contests
Problem Statement
For all reals
x
x
x
define
{
x
}
\{x\}
{
x
}
to be the difference between
x
x
x
and the closest integer to
x
x
x
. For each positive integer
n
n
n
evaluate :
S
n
=
∑
m
=
1
6
n
−
1
min
(
{
m
6
n
}
,
{
m
3
n
}
)
S_n=\sum_{m=1}^{6n-1}\min \left(\left\{\frac{m}{6n}\right\},\left\{\frac{m}{3n}\right\}\right)
S
n
=
m
=
1
∑
6
n
−
1
min
(
{
6
n
m
}
,
{
3
n
m
}
)
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