Answer
$\dfrac{5}{6}$
Work Step by Step
The sum of a geometric series can be found as:
$S=\dfrac{a}{1-r}$
The given series $\lim\limits_{n \to \infty} \cos \pi n= (-1)^n$ has first term, $a=1$ and common ratio $r =\dfrac{-1}{5}$
Thus, $S=\dfrac{1}{1-(\dfrac{-1}{5})}=\dfrac{5}{6}$