College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 9 - Section 9.3 - Geometric Sequences; Geometric Series - 9.3 Assess Your Understanding - Page 664: 45



Work Step by Step

There is a common ratio between terms, $r=2.$ The terms of the sum form a geometric sequence, $a_{1}=-1,\ r=2.$ We can write the sum as $S=\displaystyle \sum_{k=1}^{n}(-1)\cdot 2^{k-1}$ Apply THEOREM: Sum of the First $n$ Terms of a Geometric Sequence $S_{n}=\displaystyle \sum_{k=1}^{n}a_{1}r^{k-1}=a_{1}\cdot\frac{1-r^{n}}{1-r},\quad r\neq 0,1$ $=-1\displaystyle \left(\frac{1-2^{n}}{1-2}\right)$ $=-1\displaystyle \left(\frac{1-2^{n}}{-1}\right)$ $=1-2^{n}$
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.