College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 7 - Section 7.1 - Sequences and Series - 7.1 Exercises - Page 635: 39

Answer

$\dfrac{728}{9}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To evaluate the given summation expression, $ \displaystyle\sum_{i=-2}^3 2(3)^i ,$ substitute $ i $ with the values from $ -2 $ to $ 3 $ and then simplify the expression. $\bf{\text{Solution Details:}}$ Substituting $ i $ with the numbers from $ -2 $ to $ 3 ,$ the given expression evaluates to \begin{array}{l}\require{cancel} 2(3)^{-2}+2(3)^{-1}+2(3)^0+2(3)^1+2(3)^2+2(3)^3 \\\\= \dfrac{2}{3^2}+\dfrac{2}{3^1}+2(1)+2(3)+2(9)+2(27) \\\\= \dfrac{2}{9}+\dfrac{2}{3}+2+6+18+54 \\\\= \dfrac{2}{9}+\dfrac{6}{9}+\dfrac{18}{9}+\dfrac{54}{9}+\dfrac{162}{9}+\dfrac{486}{9} \\\\= \dfrac{728}{9} .\end{array}
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