Answer
$x-x^{2}+x^{3}-x^{4}+...+(-1)^{n+1}x^{n}$
Work Step by Step
We expand the sum:
$\sum_{j=1}^{n}(-1)^{j+1}x^{j}=(-1)^{2}x^1+(-1)^{3}x^{2}+(-1)^{4}x^{3}+(-1)^{5}x^{4}+\cdots+(-1)^{n+1}x^{n}=x-x^{2}+x^{3}-x^{4}+...+(-1)^{n+1}x^{n}$
College Algebra 7th Edition
by Stewart, James; Redlin, Lothar; Watson, Saleem
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 - Page 601: 66
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