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5
2016 General #5: Sequences
2016 General #5: Sequences
Source:
November 15, 2016
HMMT
Problem Statement
Let the sequence
{
a
i
}
i
=
0
∞
\{a_i\}^\infty_{i=0}
{
a
i
}
i
=
0
∞
be defined by
a
0
=
1
2
a_0 =\frac12
a
0
=
2
1
and
a
n
=
1
+
(
a
n
−
1
−
1
)
2
a_n = 1 + (a_{n-1} - 1)^2
a
n
=
1
+
(
a
n
−
1
−
1
)
2
. Find the product
∏
i
=
0
∞
a
i
=
a
0
a
1
a
2
…
\prod_{i=0}^\infty a_i=a_0a_1a_2\ldots
i
=
0
∏
∞
a
i
=
a
0
a
1
a
2
…
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