Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 8 - Sequences and Infinite Series - 8.1 An Overview - 8.1 Exercises - Page 605: 33


$a_1 = \frac{1}{10}$ $a_2 = \frac{1}{100}$ $a_3 = \frac{1}{1000}$ $a_4 = \frac{1}{10000}$ Converges. The limit seems to be $0$.

Work Step by Step

$a_n = \frac{1}{10^n}$ $a_1 = \frac{1}{10^1} = \frac{1}{10}$ $a_2 = \frac{1}{10^2} = \frac{1}{100}$ $a_3 = \frac{1}{10^3} = \frac{1}{1000}$ $a_4 = \frac{1}{10^4} = \frac{1}{10000}$ It seems to converge and appear $0$. The values are decreasing as $n$ increases, but given the equation, we know that a negative value is impossible.
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