The value of \( \lim _{n \rightarrow \infty} \frac{\pi}{n}\left[\sin \frac{\pi}{n}+\sin \frac{2 \pi}{n}+\ldots \ldots+\sin \frac{(n-1) \pi}{n}\right] \) is
This is a Riemann sum: \(\lim_{n \to \infty}\frac{\pi}{n}\sum_{k=1}^{n-1}\sin\frac{k\pi}{n} = \int_0^\pi \sin x\,dx\)
\(= [-\cos x]_0^\pi = 1 + 1 = 2\)
Answer: (C) 2
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