## University Calculus: Early Transcendentals (3rd Edition)

Consider $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty} n\pi \cos (n \pi)$ Since, $\cos (n \pi)=\pm 1$; value depends on the value of $n$ Thus, $\lim\limits_{n \to \infty} n\pi \cos (n \pi)= n\pi (-1)^n$ Hence, the Limit Does Not Exist.