University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 5 - Section 5.2 - Sigma Notation and Limits of Finite Sums - Exercises - Page 299: 18


a) 0 b) 250 c) n d) 1-n

Work Step by Step

a) \begin{equation}\sum_{k=1}^{n}8a_{k}=8\sum_{k=1}^{n}a_{k}=8\times0=0\end{equation} b) \begin{equation}\sum_{k=1}^{n}250b_{k}=250\sum_{k=1}^{n}b_{k}=250\times1=250\end{equation} c) \begin{equation}\sum_{k=1}^{n}(a_{k}+1)=\sum_{k=1}^{n}a_{k}+\sum_{k=1}^{n}1=0+1(n-1+1)=n\end{equation} d) \begin{equation}\sum_{k=1}^{n}(b_{k}-1)=\sum_{k=1}^{n}b_{k}-\sum_{k=1}^{n}1=1-1(n-1+1)=1-n\end{equation}
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