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Mathematics
Mathematics
Problem
If
∑
n
=
0
∞
2
arccot
(
n
2
+
n
+
4
2
)
=
k
π
\sum_{n=0}^{\infty} 2 \operatorname{arccot}\left(\frac{n^2+n+4}{2}\right) = k\pi
∑
n
=
0
∞
2
arccot
(
2
n
2
+
n
+
4
)
=
k
π
, then find the value of
k
k
k
.
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