Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 9 - Infinite Series - 9.2 Exercises - Page 601: 55


Please see step-by-step

Work Step by Step

See Definitions of Convergent and Divergent Series (page 595). For the infinite series $\displaystyle \sum_{n=1}^{\infty}a_{n}$, the nth partial sum is $ S_{n}=a_{1}+a_{2}+\cdot \cdot +a_{n}$. If the sequence of partial sums $\{S_{n}\}$ converges to $S$, then the series $\displaystyle \sum_{n=1}^{\infty}a_{n}$ converges. The limit $S$ is called the sum of the series. $S=a_{1}+a_{2}+... +a_{n}+...,\displaystyle \qquad S=\sum_{n=1}^{\infty}a_{n}$ If $\{S_{n}\}$ diverges, then the series diverges.
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.