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National and Regional Contests
Greece Contests
Greece National Olympiad
2013 Greece National Olympiad
1
Real sequence
Real sequence
Source: Greek MO 2013 - P1
May 12, 2013
induction
algebra proposed
algebra
Problem Statement
Let the sequence of real numbers
(
a
n
)
,
n
=
1
,
2
,
3...
(a_n),n=1,2,3...
(
a
n
)
,
n
=
1
,
2
,
3...
with
a
1
=
2
a_1=2
a
1
=
2
and
a
n
=
(
n
+
1
n
−
1
)
(
a
1
+
a
2
+
.
.
.
+
a
n
−
1
)
,
n
≥
2
a_n=\left(\frac{n+1}{n-1} \right)\left(a_1+a_2+...+a_{n-1} \right),n\geq 2
a
n
=
(
n
−
1
n
+
1
)
(
a
1
+
a
2
+
...
+
a
n
−
1
)
,
n
≥
2
. Find the term
a
2013
a_{2013}
a
2013
.
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