College Algebra (10th Edition)

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

Chapter 9 - Section 9.1 - Sequences - 9.1 Assess Your Understanding - Page 647: 53


$1+\displaystyle \frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\cdots+\frac{1}{3^{n}}$

Work Step by Step

There are n+1 terms, as the index k changes from 0 to n. The index k dictates how the terms are formed: $\displaystyle \sum_{k=0}^{n}\frac{1}{3^{k}}=\frac{1}{3^{0}}+\frac{1}{3^{1}}+\frac{1}{3^{2}}+\frac{1}{3^{3}}+...+\frac{1}{3^{n}}$ $=1+\displaystyle \frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\cdots+\frac{1}{3^{n}}$
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