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Putnam
1969 Putnam
A6
Putnam 1969 A6
Putnam 1969 A6
Source: Putnam 1969
March 31, 2022
Putnam
Convergence
Problem Statement
Let a sequence
(
x
n
)
(x_n)
(
x
n
)
be given and let
y
n
=
x
n
−
1
+
2
x
n
y_n = x_{n-1} +2 x_n
y
n
=
x
n
−
1
+
2
x
n
for
n
>
1.
n>1.
n
>
1.
Suppose that the sequence
(
y
n
)
(y_n)
(
y
n
)
converges. Prove that the sequence
(
x
n
)
(x_n)
(
x
n
)
converges, too.
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