College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 8, Sequences and Series - Section 8.1 - Sequences and Summation Notation - 8.1 Exercises: 74

Answer

$\sum_{k=1}^{100}(-1)^{k+1}* k* x^{k-1}$

Work Step by Step

We write the sum in sigma notation: (We notice that the terms have the form $(integer)x^{integer-1}$ with consecutive integers and alternating signs.) $1-2x+3x^{2}-4x^{3}+5x^{4}+ \cdots-100x^{99}=\sum_{k=1}^{100}(-1)^{k+1}* k* x^{k-1}$
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