University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 9 - Section 9.1 - Sequences - Exercises - Page 488: 61

Answer

Converges to $4$

Work Step by Step

Consider $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty} \sqrt [n] {4^n n}$ Since, $\lim\limits_{n \to \infty} \sqrt[n] {n}=1$ and $\lim\limits_{n \to \infty} x^{1/n}=1$ when $x \gt 0$ So, $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty} \sqrt [m] {4^n n}=4 \lim\limits_{n \to \infty}\sqrt [n] {n} =(4)(1)=4$ Hence, $\lim\limits_{n \to \infty} a_n=4$ and {$a_n$} is Convergent and converges to $4$
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