Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 12 - Sequences; Induction; the Binomial Theorem - Chapter Review - Review Exercises - Page 839: 15

Answer

$\dfrac{1093}{2187}$

Work Step by Step

We have to determine the sum: $\sum_{k=1}^7 \left(\dfrac{1}{3}\right)^k$ Consider the geometric sequence: $a_1=\left(\dfrac{1}{3}\right)^1=\dfrac{1}{3}$ $r=\dfrac{1}{3}$ Compute the sum of the first 7 terms: $S_n=a_1\dfrac{1-r^n}{1-r}$ $n=7$ $\sum_{k=1}^7 \left(\dfrac{1}{3}\right)^k=S_7=\dfrac{1}{3}\cdot\dfrac{1-\left(\dfrac{1}{3}\right)^7}{1-\dfrac{1}{3}}$ $=\dfrac{1}{3}\cdot \left(1-\dfrac{1}{2187}\right)\cdot\dfrac{3}{2}=\dfrac{2186}{2(2187)}=\dfrac{1093}{2187}$
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.