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Bundeswettbewerb Mathematik
2000 Bundeswettbewerb Mathematik
4
Can the sum be equal to zero? [Germany BW 2000]
Can the sum be equal to zero? [Germany BW 2000]
Source:
February 3, 2011
geometry
3D geometry
algebra proposed
algebra
Problem Statement
Consider the sums of the form
∑
k
=
1
n
ϵ
k
k
3
,
\sum_{k=1}^{n} \epsilon_k k^3,
∑
k
=
1
n
ϵ
k
k
3
,
where
ϵ
k
∈
{
−
1
,
1
}
.
\epsilon_k \in \{-1, 1\}.
ϵ
k
∈
{
−
1
,
1
}
.
Is any of these sums equal to
0
0
0
if(a)
n
=
2000
;
n=2000;
n
=
2000
;
(b)
n
=
2001
?
n=2001 \ ?
n
=
2001
?
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