MathDB
Problems
Contests
National and Regional Contests
Indonesia Contests
Indonesia TST
2010 Indonesia TST
1
Nice sequence...
Nice sequence...
Source: 2nd Test - Indonesia TST IMO 2010 Training Camp P1
February 22, 2017
Sequence
algebra
Problem Statement
Sequence
u
n
{u_n}
u
n
is defined with
u
0
=
0
,
u
1
=
1
3
u_0=0,u_1=\frac{1}{3}
u
0
=
0
,
u
1
=
3
1
and
2
3
u
n
=
1
2
(
u
n
+
1
+
u
n
−
1
)
\frac{2}{3}u_n=\frac{1}{2}(u_{n+1}+u_{n-1})
3
2
u
n
=
2
1
(
u
n
+
1
+
u
n
−
1
)
∀
n
=
1
,
2
,
.
.
.
\forall n=1,2,...
∀
n
=
1
,
2
,
...
Show that
∣
u
n
∣
≤
1
|u_n|\leq1
∣
u
n
∣
≤
1
∀
n
∈
N
.
\forall n\in\mathbb{N}.
∀
n
∈
N
.
Back to Problems
View on AoPS