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Problem
Problem
Number of solutions of the equation
csc
θ
=
k
\csc \theta = k
csc
θ
=
k
in
[
0
,
π
]
[0, \pi]
[
0
,
π
]
, where
k
=
lim
n
→
∞
π
∑
r
=
2
n
(
r
3
−
1
r
3
+
1
)
k = \lim_{n \to \infty} \pi \sum_{r=2}^{n} \left( \frac{r^3 - 1}{r^3 + 1} \right)
k
=
lim
n
→
∞
π
∑
r
=
2
n
(
r
3
+
1
r
3
−
1
)
, is .....
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