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2023 JBMO Shortlist
A6
A6
Part of
2023 JBMO Shortlist
Problems
(1)
JBMO Shortlist 2023 A6
Source: JBMO Shortlist 2023, A6
6/28/2024
Find the maximum constant
C
C
C
such that, whenever
{
a
n
}
n
=
1
∞
\{a_n \}_{n=1}^{\infty}
{
a
n
}
n
=
1
∞
is a sequence of positive real numbers satisfying
a
n
+
1
−
a
n
=
a
n
(
a
n
+
1
)
(
a
n
+
2
)
a_{n+1}-a_n=a_n(a_n+1)(a_n+2)
a
n
+
1
−
a
n
=
a
n
(
a
n
+
1
)
(
a
n
+
2
)
, we have
a
2023
−
a
2020
a
2022
−
a
2021
>
C
.
\frac{a_{2023}-a_{2020}}{a_{2022}-a_{2021}}>C.
a
2022
−
a
2021
a
2023
−
a
2020
>
C
.
Sequence
inequalities
JBMO
JBMO Shortlist
algebra