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Putnam
2014 Putnam
3
Putnam 2014 A3
Putnam 2014 A3
Source:
December 7, 2014
Putnam
limit
induction
inequalities
algebra
difference of squares
Putnam 2014
Problem Statement
Let
a
0
=
5
/
2
a_0=5/2
a
0
=
5/2
and
a
k
=
a
k
−
1
2
−
2
a_k=a_{k-1}^2-2
a
k
=
a
k
−
1
2
−
2
for
k
≥
1.
k\ge 1.
k
≥
1.
Compute
∏
k
=
0
∞
(
1
−
1
a
k
)
\prod_{k=0}^{\infty}\left(1-\frac1{a_k}\right)
k
=
0
∏
∞
(
1
−
a
k
1
)
in closed form.
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