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: 34

Answer

$a_1 = \frac{1}{10}$ $a_2 = \frac{1}{100}$ $a_3 = \frac{1}{1000}$ $a_4 = \frac{1}{10000}$ Converges. The limit of the sequence is $0$.

Work Step by Step

$a_{n+1} = \frac{a_n}{10}$; $a_0 = 1$ $a_1 = \frac{a_0}{10} = \frac{1}{10}$ $a_2 = \frac{a_1}{10} = \frac{1}{100}$ $a_3 = \frac{a_2}{10} = \frac{1}{1000}$ $a_4 = \frac{a_3}{10} = \frac{1}{10000}$ Converges and approaches zero. The values of the sequence are decreasing, but given the equation, cannot be negative.
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