Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 5 - The Integral - 5.1 Approximating and Computing Area - Exercises - Page 235: 30


(a) -1 (b) $\frac{13}{12}$ (c) $\frac{13}{3}$

Work Step by Step

(a) \begin{equation}\sum_{j=3}^{4}\sin(j\frac{\pi}{2})=\sin(3\frac{\pi}{2})+\sin(4\frac{\pi}{2})=\sin(\frac{3\pi}{2})+\sin 2\pi=-1+0=-1\end{equation} (b) \begin{equation}\sum_{k=3}^{5}\frac{1}{k-1}=\frac{1}{3-1}+\frac{1}{4-1}+\frac{1}{5-1}=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}=\frac{13}{12}\end{equation} (c) \begin{equation}\sum_{j=0}^{2}3^{j-1}=3^{0-1}+3^{1-1}+3^{2-1}=3^{-1}+3^{0}+3^{1}=\frac{1}{3}+1+3=\frac{13}{3}\end{equation}
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