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Francophone Mathematical Olympiad
2020 Francophone Mathematical Olympiad
3
Find n for which k<=a_n<k+1
Find n for which k<=a_n<k+1
Source: The francophone mathematical olympiads P3
June 27, 2020
Sequence
algebra
Francophone
Problem Statement
Let
(
a
i
)
i
∈
N
(a_i)_{i\in \mathbb{N}}
(
a
i
)
i
∈
N
be a sequence with
a
1
=
3
2
a_1=\frac{3}2
a
1
=
2
3
such that
a
n
+
1
=
1
+
n
a
n
a_{n+1}=1+\frac{n}{a_n}
a
n
+
1
=
1
+
a
n
n
Find
n
n
n
such that
2020
≤
a
n
<
2021
2020\le a_n <2021
2020
≤
a
n
<
2021
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