Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Appendix E - Sigma Notation - E Exercises: 20

Answer

$\sum_{i=0}^{n}(-1)^{i}x^{i}$

Work Step by Step

We contract the sum into sigma notation by noting that it follows the pattern of a sum of powers of $x$ (e.g. $x^i$), starting with $1=x^0$ (e.g. $i=0$) and ending with $x^n$ (e.g. $i=n$). In addition, the sign of the terms alternates, so we include $(-1)^n$: $1-x+x^{2}-x^{3}+\displaystyle \cdots+(-1)^{n}x^{n}=\sum_{i=0}^{n}(-1)^{i}x^{i}$
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