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: 44

Answer

$$\sum_{k=1}^{5} (-1)^{k+1}(k^3-1)$$

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 $(-1)^{k+1}$ will be used. The terms of the summation is of the form $(k^3-1)$ where $k$ is a counting number starting with $1$. The summation has 5 terms so $k$ is from 1 to 5 only. Thus, the summation notation whose expanded form is given is: $$\sum_{k=1}^{5} (-1)^{k+1}(k^3-1)$$
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