Let $1, \zeta_2, \zeta_3, \ldots, \zeta_n$ be the roots of the equation $x^n=1$, for $n \geq 3$. Then, the sum
$\frac{1}{2-\zeta_2}+\frac{1}{2-\zeta_3}+\cdots+\frac{1}{2-\zeta_n}$
equals to

• A

  $\frac{1+(n-2) 2^n}{2^n-1}$.
• Correct answer
  B

  $\frac{1+n 2^{n-1}-2^n}{2^n-1}$.
• C

  $\frac{1+n 2^{n-1}-2^n}{2^{n-1}+1}$.
• D

  $\frac{1+(n-1) 2^n-2^{n-1}}{2^{n-1}+1}$.

Hence, the correct answer is option: 'B'.