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National and Regional Contests
Korea Contests
Korea National Olympiad
1996 Korea National Olympiad
3
3
Part of
1996 Korea National Olympiad
Problems
(1)
floor + sum
Source: 1996 Korea National Olympiad #3
3/22/2018
Let
a
=
⌊
n
⌋
a=\lfloor \sqrt{n} \rfloor
a
=
⌊
n
⌋
for given positive integer
n
.
n.
n
.
Express the summation
∑
k
=
1
n
⌊
k
⌋
\sum_{k=1}^{n}\lfloor \sqrt{k} \rfloor
∑
k
=
1
n
⌊
k
⌋
in terms of
n
n
n
and
a
.
a.
a
.
floor function
algebra