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: 53


Converges to $e^7$

Work Step by Step

Consider $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty} (1+\dfrac{7}{n})^{n}$ Since, $\lim\limits_{n \to \infty} (1+\dfrac{x}{n})^{n}=e^x$ when $x \gt 0$ So, $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty} (1+\dfrac{7}{n})^{n}=e^7$ Hence, $\lim\limits_{n \to \infty} a_n=e^7 $ and {$a_n$} is convergent and converges to $e^7$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.