The value of is equal to

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

The value of lim⁡n→∞(sin⁡π2n⋅sin⁡2π2n⋅sin⁡3π2n…sin⁡(n−1)πn)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} is equal to (1) 12\frac{1}{2} (2) 13\frac{1}{3} (3) 14\frac{1}{4} (4) None of these

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