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: 13

Answer

$\sum_{i=1}^{19}\frac{i}{i+1}$

Work Step by Step

We contract the sum into sigma notation by noting that it follows the pattern of a sum of fractions with integers 1-19 on top and a denominator increased by 1 (e.g. $\frac{i}{i+1}$): $\displaystyle \frac{1}{2}+\frac{2}{3}+\frac{3}{4}+\frac{4}{5}+\cdots+\frac{19}{20}=\sum_{i=1}^{19}\frac{i}{i+1}$
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