College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 8, Sequences and Series - Chapter 8 Review - Exercises - Page 640: 41

Answer

$0^2+1^2+2^2+3^2+4^2+5^2+6^2+7^2+8^2+9^2$

Work Step by Step

We rewrite the given sum by expanding it: in each term $(k-1)^2$ substitute the values of $k$, where $k=1,2,\dots,10$: $$\begin{align*} \sum_{k=1}^{10} (k-1)^2&=(1-1)^2+(2-1)^2+(3-1)^2+(4-1)^2+(5-1)^2+(6-1)^2+(7-1)^2+(8-1)^2+(9-1)^2+(10-1)^2\\ &=0^2+1^2+2^2+3^2+4^2+5^2+6^2+7^2+8^2+9^2. \end{align*}$$
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