If $\mathrm{C}_0, \mathrm{C}_1, \mathrm{C}_2, \ldots, \mathrm{C}_{\mathrm{n}}$ are the binomial coefficients in the expansion of $(1+\mathrm{x})^{\mathrm{n}}$, then $\left(\mathrm{C}_0+\mathrm{C}_1\right)-\left(\mathrm{C}_2+\mathrm{C}_3\right)+\left(\mathrm{C}_4+\mathrm{C}_5\right)-\left(\mathrm{C}_6+\mathrm{C}_7\right)+\ldots=$

• A

  $2^{n / 2}\left(\cos \frac{n \pi}{4}+i \sin \frac{n \pi}{4}\right)$
• B

  $2^{n / 2}\left(\cos \frac{n \pi}{3}+\sin \frac{n \pi}{3}\right)$
• C

  $2^{n / 2}\left(\cos \frac{n \pi}{3}+i \sin \frac{n \pi}{3}\right)$
• Correct answer
  D

  $2^{n / 2}\left(\cos \frac{n \pi}{4}+\sin \frac{n \pi}{4}\right)$

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