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 - Preliminary Questions - Page 234: 4


See details below.

Work Step by Step

The sums $$\sum_{j=1}^{100} j, \quad\sum_{j=0}^{100} j $$ are equal because the extra term in the second sum is just $0$ and when you add zero to a value that value will remain unchanged. But the sums $$\sum_{j=1}^{100} 1, \quad\sum_{j=0}^{100} $$ are not equal because the extra term is equal to $1$ and this creates the difference.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.