## Thomas' Calculus 13th Edition

The function $\cos x$ always oscillates in between $-1$ and $+1$. This implies that it does not have any limit and lso, $\cos \pi n=1$; for even value of $n$ and $\cos \pi n=-1$; for odd values of $n$ Thus, $\lim\limits_{n \to \infty} \cos \pi n$= Limit does not exist or divergent. Hence, the series diverges.