College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 9 - Section 9.1 - Sequences - 9.1 Assess Your Understanding - Page 647: 60

Answer

$1^{3}+2^{3}+3^{3}+\displaystyle \cdots+8^{3}=\sum_{k=1}^{8}k^{3}$

Work Step by Step

$1^{3}+2^{3}+3^{3}+\cdots+8^{3}=$ There are 8 terms, count them with index k: $\displaystyle \sum_{k=1}^{8}$(...) The first term (when k=1) is $1^{3}$, The second term (when k=2) is $2^{3}$, The kth is $k^{3}$ so $1^{3}+2^{3}+3^{3}+\displaystyle \cdots+8^{3}=\sum_{k=1}^{8}k^{3}$
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