Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

APPENDIX E - Sigma Notation - E Exercises: 18

Answer

$\displaystyle \sum_{i=1}^{6}\frac{1}{i^{2}}$

Work Step by Step

We contract the sum into sigma notation by noting that it follows the pattern of a sum of fractions with 1 on top and squares of integers on the bottom (e.g. $\frac{1}{i^2}$), starting with $\frac{1}{1}$ (e.g. $i=1$), and ending with $\frac{1}{36}$ (e.g. $i=6$). $\displaystyle \frac{1}{1}+\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+\frac{1}{25}+\frac{1}{36}=\sum_{i=1}^{6}\frac{1}{i^{2}}$
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