Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 10: Infinite Sequences and Series - Section 10.1 - Sequences - Exercises 10.1 - Page 570: 51


converges to $1$.

Work Step by Step

Let $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty} (8)^{\frac{1}{n}}$ as we know that $\lim\limits_{n \to \infty} x^{\frac{1}{n}}=1$ when $x \gt 0$ This shows that the limit has an indeterminate form so we will use L-Hospital's rule. This implies that $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty} (8)^{\frac{1}{n}}=1$ Thus, $\lim\limits_{n \to \infty} a_n=1 $ converges to $1$.
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