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PEN M Problems
7
M 7
M 7
Source:
May 25, 2007
induction
quadratics
algebra
Recursive Sequences
Problem Statement
Prove that the sequence
{
y
n
}
n
≥
1
\{y_{n}\}_{n \ge 1}
{
y
n
}
n
≥
1
defined by
y
0
=
1
,
y
n
+
1
=
1
2
(
3
y
n
+
5
y
n
2
−
4
)
y_{0}=1, \; y_{n+1}= \frac{1}{2}\left( 3y_{n}+\sqrt{5y_{n}^{2}-4}\right)
y
0
=
1
,
y
n
+
1
=
2
1
(
3
y
n
+
5
y
n
2
−
4
)
consists only of integers.
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