If \( 1, z_{1}, z_{2}, z_{3}, \ldots, z_{n-1} \) are the \( n, n \)th roots of unity, then the v...

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If \( 1, z_{1}, z_{2}, z_{3}, \ldots, z_{n-1} \) are the \( n, n \)th roots of unity, then the value of \( \sum_{r=1}^{n-1} \frac{1}{\left(3-z_{r}\right)} \), is
(a) \( \frac{n \cdot 3^{n-1}}{3^{n}-1}+\frac{1}{2} \)
(b) \( \frac{n \cdot 3^{n-1}}{3^{n}-1}-1 \)
(c) \( \frac{n \cdot 3^{n-1}}{3^{n}-1}+1 \)
(d) None of these
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