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: 80


Converges to $5$

Work Step by Step

Consider $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} (3^n +5^n)^{1/n}$ Since, $ \lim\limits_{n \to \infty} x^{1/n}=1$ when $x \gt 0$ So, $ \lim\limits_{n \to \infty} 5((\dfrac{3}{5})^n+1)^n=5$ Hence, $\lim\limits_{n \to \infty} a_n=5$ and {$a_n$} is Convergent and converges to $5$
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