Thomas' Calculus 13th Edition

$\dfrac{5}{6}$
Formula to calculate the sum of a geometric series is:$S=\dfrac{a}{1-r}$ Consider the series $\lim\limits_{n \to \infty} \cos \pi n= (-1)^n$ with first term, $a=1$ and common ratio $r =\dfrac{-1}{5}$ Hence, $S=\dfrac{a}{1-r}=\dfrac{1}{1-(\dfrac{-1}{5})}$ or $S=\dfrac{5}{6}$