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: 36

Answer

$a_1 = 0.9$ $a_2 = 0.99$ $a_3 = 0.999$ $a_4 = 0.9999$ Converges. The limit of the sequence seems to be $1$.

Work Step by Step

$a_n = 1-10^{-n}$ $a_1 = 1 - 10^{-1} = 0.9$ $a_2 = 1 - 10^{-2} = 0.99$ $a_3 = 1 - 10^{-3} = 0.999$ $a_4 = 1 - 10^{-4} = 0.9999$ Converges and approaches $1$. The term $10^{-n}$ seems to approach zero as $n$ increases and $1-0=1$. Alternatively, simply looking at the terms tells us that the term approaches $1$ as $n$ increases.
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.