Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 11 - Section 11.1 - Sequences - 11.1 Exercises: 32

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.
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