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China Contests
China Northern MO
2017 China Northern MO
1
2017 CNMO Grade 11 P1
2017 CNMO Grade 11 P1
Source: 2017 China Northern MO, Grade 11, Problem 1
February 24, 2020
algebra
Problem Statement
Define sequence
(
a
n
)
:
a
1
=
e
,
a
2
=
e
3
,
e
1
−
k
a
n
k
+
2
=
a
n
+
1
a
n
−
1
2
k
(a_n):a_1=\text{e},a_2=\text{e}^3,\text{e}^{1-k}a_n^{k+2}=a_{n+1}a_{n-1}^{2k}
(
a
n
)
:
a
1
=
e
,
a
2
=
e
3
,
e
1
−
k
a
n
k
+
2
=
a
n
+
1
a
n
−
1
2
k
for all
n
≥
2
n\geq2
n
≥
2
, where
k
k
k
is a positive real number. Find
∏
i
=
1
2017
a
i
\prod_{i=1}^{2017}a_i
∏
i
=
1
2017
a
i
.
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