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Putnam
1947 Putnam
A1
Putnam 1947 A1
Putnam 1947 A1
Source: Putnam 1947
April 3, 2022
Putnam
Sequence
limit
Problem Statement
If
(
a
n
)
(a_n)
(
a
n
)
is a sequence of real numbers such that for
n
≥
1
n \geq 1
n
≥
1
(
2
−
a
n
)
a
n
+
1
=
1
,
(2-a_n )a_{n+1} =1,
(
2
−
a
n
)
a
n
+
1
=
1
,
prove that
lim
n
→
∞
a
n
=
1.
\lim_{n\to \infty} a_n =1.
lim
n
→
∞
a
n
=
1.
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