Answer
The sequence converges to $\cos{(\pi)} = -1$.
Work Step by Step
By continuity of limits we may take the limit inside of the cosine function. Since the highest exponent in the numerator matches the highest exponent in the denominator, the limit of the inside is that of $\frac{\pi n}{n} = \pi$. Thus the sequence converges to $\cos{(\pi)}$ = -1.
