Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 14 - Sequences, Series, and the Binomial Theorem - 14.1 Sequences and Series - 14.1 Exercise Set - Page 895: 71

Answer

$\sum\limits_{k=2}^{n}{{{\left( -1 \right)}^{k}}{{k}^{2}}}.$

Work Step by Step

$4-9+16-25+\ldots +{{\left( -1 \right)}^{n}}{{n}^{2}}$ This is the sum of the square of the natural numbers, and the sum alternates between positive and negative. The value of $k$ varies from $k=2$ to $k=n$. Thus, the sigma notation is, $\sum\limits_{k=2}^{n}{{{\left( -1 \right)}^{k}}{{k}^{2}}}$ Thus, the sigma notation for the sum$4-9+16-25+\ldots +{{\left( -1 \right)}^{n}}{{n}^{2}}$ is $\sum\limits_{k=2}^{n}{{{\left( -1 \right)}^{k}}{{k}^{2}}\text{ }}$.
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