Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Appendix E - Sigma Notation - E Exercises: 40

Answer

$i^{3}$

Work Step by Step

Area for $G_{i}=[\frac{i(i+1)}{2}]^{2}-[\frac{i(i-1)}{2}]^{2}$ $=\frac{i^{2}(i+1)^{2}}{4}-\frac{i^{2}(i-1)^{2}}{4}$ $=\frac{1}{4}i^{2}[(i+1)^{2}-(i-1)^{2}]$ $=\frac{1}{4}i^{2}[4i]$ Hence, the area for $G_{i}=i^{3}$
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