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Thailand TST Selection Test
2018 Thailand TSTST
7
Sum of fractional part of binomial coefficients
Sum of fractional part of binomial coefficients
Source: 2017 Thailand October Camp 1.7
February 25, 2022
binomial coefficients
algebra
function
Problem Statement
Evaluate
∑
n
=
2017
2030
∑
k
=
1
n
{
(
n
k
)
2017
}
\sum_{n=2017}^{2030}\sum_{k=1}^{n}\left\{\frac{\binom{n}{k}}{2017}\right\}
∑
n
=
2017
2030
∑
k
=
1
n
{
2017
(
k
n
)
}
.Note:
{
x
}
=
x
−
⌊
x
⌋
\{x\}=x-\lfloor x\rfloor
{
x
}
=
x
−
⌊
x
⌋
for every real numbers
x
x
x
.
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