MathDB
Problems
Contests
National and Regional Contests
Japan Contests
Japan TST
2017 Japan TST
8
8
Part of
2017 Japan TST
Problems
(1)
Prove sequence is bounded
Source: Japan TST 2017 P8
1/24/2021
A sequence of positive integers
a
1
,
a
2
,
…
a_1,a_2,\ldots
a
1
,
a
2
,
…
satisfies
a
n
>
a
n
+
1
+
a
n
+
2
+
…
+
a
2
n
n
+
2016
a_n > \frac{a_{n+1}+a_{n+2}+\ldots +a_{2n}}{n+2016}
a
n
>
n
+
2016
a
n
+
1
+
a
n
+
2
+
…
+
a
2
n
for all positive integers
n
n
n
. Show that there exists a positive real
C
C
C
such that
a
n
<
C
a_n<C
a
n
<
C
for all positive integers
n
n
n
.
algebra
Sequence
inequalities