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Putnam
1986 Putnam
A3
A3
Part of
1986 Putnam
Problems
(1)
Putnam 1986 A3
Source:
8/5/2019
Evaluate
∑
n
=
0
∞
A
r
c
c
o
t
(
n
2
+
n
+
1
)
\textstyle\sum_{n=0}^\infty \mathrm{Arccot}(n^2+n+1)
∑
n
=
0
∞
Arccot
(
n
2
+
n
+
1
)
, where
A
r
c
c
o
t
t
\mathrm{Arccot}\,t
Arccot
t
for
t
≥
0
t \geq 0
t
≥
0
denotes the number
θ
\theta
θ
in the interval
0
<
θ
≤
π
/
2
0 < \theta \leq \pi/2
0
<
θ
≤
π
/2
with
cot
θ
=
t
\cot \theta = t
cot
θ
=
t
.
Putnam