The limit $\lim_{n \to \infty} \sum_{k = 1}^n \left| e^{\frac{2\pi ik}{n}} − e^{\frac{2\pi i(k-1)}{n}} \right|$ is
(A) $2$
(B) $2e$
(C) $2\pi$
(D) $2i$.
I can't solve this problem. Do I need to use $e^{i\theta} = \cos \theta + i \sin \theta$ or do I need some other formula to proceed? I don't understand that is I need to interchange the limit and summation. Please help me. This is a multiple choice question from a sample test paper of ISI MSTAT examination.