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Putnam
2020 Putnam
A3
A3
Part of
2020 Putnam
Problems
(1)
Putnam 2020 A3
Source: 81st William Lowell Putnam Competition
2/22/2021
Let
a
0
=
π
/
2
a_0=\pi /2
a
0
=
π
/2
, and let
a
n
=
sin
(
a
n
−
1
)
a_n=\sin (a_{n-1})
a
n
=
sin
(
a
n
−
1
)
for
n
≥
1
n\ge 1
n
≥
1
. Determine whether
∑
n
=
1
∞
a
n
2
\sum_{n=1}^{\infty}a_n^2
n
=
1
∑
∞
a
n
2
converges.
Putnam
Putnam 2020
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