MathDB
Problems
Contests
National and Regional Contests
China Contests
(China) National High School Mathematics League
2011 China Second Round Olympiad
10
10
Part of
2011 China Second Round Olympiad
Problems
(1)
sequence a_n
Source: China Second Round Test1
1/30/2012
A sequence
a
n
a_n
a
n
satisfies
a
1
=
2
t
−
3
a_1 =2t-3
a
1
=
2
t
−
3
(
t
≠
1
,
−
1
t \ne 1,-1
t
=
1
,
−
1
), and
a
n
+
1
=
(
2
t
n
+
1
−
3
)
a
n
+
2
(
t
−
1
)
t
n
−
1
a
n
+
2
t
n
−
1
a_{n+1}=\dfrac{(2t^{n+1}-3)a_n+2(t-1)t^n-1}{a_n+2t^n-1}
a
n
+
1
=
a
n
+
2
t
n
−
1
(
2
t
n
+
1
−
3
)
a
n
+
2
(
t
−
1
)
t
n
−
1
.i) Find
a
n
a_n
a
n
,ii) If
t
>
0
t>0
t
>
0
, compare
a
n
+
1
a_{n+1}
a
n
+
1
with
a
n
a_n
a
n
.
integration
algebra unsolved
algebra