Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.1 Sequences - 11.1 Assess Your Understanding - Page 827: 51

Answer

$\displaystyle \frac{1}{2}+2+\frac{9}{2}+8+\frac{25}{2}+18+\frac{49}{2}+...+\frac{n^{2}}{2}$

Work Step by Step

We see that there are $n$ terms, as the index $k$ changes from $1$ to $n$. The index $k$ indicates how the terms are formed. We write out the sum for the $n$ terms as follows: $\displaystyle \sum_{k=1}^{n}\frac{k^{2}}{2}=\frac{(1)^{2}}{2}+\frac{(2)^{2}}{2}+\frac{(3)^{2}}{2}+...+\frac{(n)^{2}}{2} \\ =\displaystyle \frac{1}{2}+2+\frac{9}{2}+8+\frac{25}{2}+18+\frac{49}{2}+...+\frac{n^{2}}{2}$
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