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2020 LMT Spring
21
Spring 2020 Team Round Problem 21
Spring 2020 Team Round Problem 21
Source:
August 22, 2020
Problem Statement
Let
{
a
n
}
\{a_n\}
{
a
n
}
be the sequence such that
a
0
=
2019
a_0=2019
a
0
=
2019
and
a
n
=
−
2020
n
∑
k
=
0
n
−
1
a
k
.
a_n=-\frac{2020}{n}\sum_{k=0}^{n-1}a_k.
a
n
=
−
n
2020
k
=
0
∑
n
−
1
a
k
.
Compute the last three digits of
∑
n
=
1
2020
202
0
n
a
n
n
\sum_{n=1}^{2020}2020^na_nn
∑
n
=
1
2020
202
0
n
a
n
n
.
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