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2013 BMT Spring
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2013 BMT Individual 20
Source:
January 18, 2022
algebra
Problem Statement
A sequence
a
n
a_n
a
n
is defined such that
a
0
=
1
+
3
2
a_0 =\frac{1 + \sqrt3}{2}
a
0
=
2
1
+
3
and
a
n
+
1
=
a
n
a_{n+1} =\sqrt{a_n}
a
n
+
1
=
a
n
for
n
≥
0
n \ge 0
n
≥
0
. Evaluate
∏
k
=
0
∞
1
−
a
k
+
a
k
2
\prod_{k=0}^{\infty} 1 - a_k + a^2_k
k
=
0
∏
∞
1
−
a
k
+
a
k
2
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