Calculus: Early Transcendentals 8th Edition

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

Chapter 11 - Section 11.2 - Series - 11.2 Exercises - Page 716: 25



Work Step by Step

The given series can be made into a similar form as the definition of the geometric series. We can reach the textbook form by inputting $n=1$ to get the initial term $a$ and see the factor difference when inputting $n=2$. Note that the summation of an infinite geometric series is $S= \frac{a}{1-r}$ if |$r$| $\lt 1 $ , here $r$ is the common ratio of the geometric series. Now, If we choose n = 1 we can see that the initial term is $a$ = $e^{2}$ and the common ratio $r$ = $\frac{e^{2}}{6}$ (Just by dividing any latter term by its former). |$r$| = $\frac{e^{2}}{6}\approx 1.232 \gt 1 $ Thus, this geometric series diverges.
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