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Problem
Problem
Find the value
lim
n
→
∞
∑
k
=
2
n
cos
−
1
(
1
+
(
k
−
1
)
k
(
k
+
1
)
(
k
+
2
)
k
(
k
+
1
)
)
\lim_{n \to \infty} \sum_{k=2}^{n} \cos^{-1} \left( \frac{1 + \sqrt{(k-1)k(k+1)(k+2)}}{k(k+1)} \right)
n
→
∞
lim
k
=
2
∑
n
cos
−
1
(
k
(
k
+
1
)
1
+
(
k
−
1
)
k
(
k
+
1
)
(
k
+
2
)
)
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