Calculus 8th Edition

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

Chapter 11 - Infinite Sequences and Series - 11.2 Series - 11.2 Exercises: 21

Answer

In this explicit form we see that $r$ =|$0.73|\lt1 $ which means that this geometric series will converge. Now, use the formula from definition 4 in page 750 , knowing that $a$ refers to the first term which is $12$ and using the explicit $r$ and we get $S= \frac{a}{1-r}$ = $\frac{12}{1-0.73} = \frac{12}{0.27} = \frac{400}{9}$ Result: the series converges and its sum is $\frac{400}{9}$ .

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