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

The value of the function $\cos x$ always oscillates in between $-1$ and $+1$. Thus, its acquires no limit and $\cos \pi n=1$ for even values of $n$ and $\cos \pi n=-1$; for odd values of $n$. Therefore, $\lim\limits_{n \to \infty} \cos \pi n$= Limit does not exist Hence, the series is divergent.