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Mathematics
Mathematics
Problem
The value of
lim
n
→
∞
(
sin
π
2
n
⋅
sin
2
π
2
n
⋅
sin
3
π
2
n
…
sin
(
n
−
1
)
π
n
)
1
/
n
\lim_{n \to \infty} \left( \sin \frac{\pi}{2n} \cdot \sin \frac{2\pi}{2n} \cdot \sin \frac{3\pi}{2n} \dots \sin \frac{(n-1)\pi}{n} \right)^{1/n}
lim
n
→
∞
(
sin
2
n
π
⋅
sin
2
n
2
π
⋅
sin
2
n
3
π
…
sin
n
(
n
−
1
)
π
)
1/
n
is equal to a.
1
2
\frac{1}{2}
2
1
b.
1
3
\frac{1}{3}
3
1
c.
1
4
\frac{1}{4}
4
1
d. None of these
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