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Cono Sur Olympiad
1996 Cono Sur Olympiad
2
2
Part of
1996 Cono Sur Olympiad
Problems
(1)
An Easy Sequence Problem
Source: Cono sur 1996, Problem 2
5/7/2018
Consider a sequence of real numbers defined by:
a
n
+
1
=
a
n
+
1
a
n
a_{n + 1} = a_n + \frac{1}{a_n}
a
n
+
1
=
a
n
+
a
n
1
for
n
=
0
,
1
,
2
,
.
.
.
n = 0, 1, 2, ...
n
=
0
,
1
,
2
,
...
Prove that, for any positive real number
a
0
a_0
a
0
, is true that
a
1996
a_{1996}
a
1996
is greater than
63
63
63
.
cono sur
Sequences