Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 11 - Section 11.1 - Sequences - 11.1 Exercises - Page 704: 22

Answer

$a_n=${2.1111, 2.2346, 2.3717, 2.5242, 2.6935, 2.8817, 3.0908, 3.323, 3.5812, 3.8680} This sequence is divergent

Work Step by Step

Given: $a_n=1+\frac{{10}^{n}}{{9}^{n}}$ Substitute the values 1 to 10 in the place of n: $a_n=${2.1111, 2.2346, 2.3717, 2.5242, 2.6935, 2.8817, 3.0908, 3.323, 3.5812, 3.8680} From inspection this sequence does not converge If you take $\frac{{10}^{n}}{{9}^{n}}$ =${(\frac{10}{9})}^{n}$ Therefore r=$\frac{10}{9}$>1 This means that it is divergent
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