MathDB
Problems
Contests
National and Regional Contests
India Contests
India IMO Training Camp
2018 India IMO Training Camp
3
Sequence gets beyond 2018
Sequence gets beyond 2018
Source: IMOTC PT1 P3 2018, India
July 18, 2018
algebra
Sequence
inequalities
Problem Statement
Let
a
n
,
b
n
a_n, b_n
a
n
,
b
n
be sequences of positive reals such that,
a
n
+
1
=
a
n
+
1
2
b
n
a_{n+1}= a_n + \frac{1}{2b_n}
a
n
+
1
=
a
n
+
2
b
n
1
b
n
+
1
=
b
n
+
1
2
a
n
b_{n+1}= b_n + \frac{1}{2a_n}
b
n
+
1
=
b
n
+
2
a
n
1
for all
n
∈
N
n\in\mathbb N
n
∈
N
. Prove that,
max
(
a
2018
,
b
2018
)
>
44
\text{max}\left(a_{2018}, b_{2018}\right) >44
max
(
a
2018
,
b
2018
)
>
44
.
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