Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 5 - Sequences, Mathematical Induction, and Recursion - Exercise Set 5.1 - Page 243: 43


$$\sum_{k=1}^{7} (-1)^{k+1}k^2$$

Work Step by Step

The sequence involves a sum with alternating signs (positive, then negative, then positive, and so on...). This means that the summation involves either $(-1)^k$ or $(-1)^{k+1}$. The first term is positive so it $-1)^{k+1}$ will be used. Each term of the sequence involves a square of counting number, starting at $1$. This means that the summation involves $k^2$. The summation has 7 terms so $k$ is from 1 to 7 only. Thus, the summation notation whose expanded form is given is: $$\sum_{k=1}^{7} (-1)^{k+1}k^2$$
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