$1+\cos x+\cos ^2 x+\cos ^3 x+\ldots$ to $\infty=4+2 \sqrt{3}$, then $x=$

• A

  $\frac{n \pi}{6}$
• B

  $(4 n \pm 1) \frac{\pi}{3}$
• Correct answer
  C

  $(12 n \pm 1) \frac{\pi}{6}$
• D

  $(3 n \pm 1) \frac{\pi}{3}$

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