Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 11 - Infinite Series - Chapter Review Exercises - Page 591: 12



Work Step by Step

We have $$ \lim _{n \rightarrow \infty} a_n=\lim _{n \rightarrow \infty}\frac{10^n}{n!}=0. $$ Since we know that for all $n\gt \gt 10$, $n!$ is getting bigger faster than $10^n$. Hence, $a_n$ converges to $0$.
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