Calculus 8th Edition

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

Chapter 11 - Infinite Sequences and Series - 11.1 Sequences - 11.1 Exercises - Page 744: 5


$\frac{1}{5},-\frac{1}{25},\frac{1}{125},-\frac{1}{625}, \frac{1}{3125}$

Work Step by Step

To find the first five terms of the sequence $a_n = \frac{(-1)^{(n-1)} }{5^n}$, we must plug in $n=1, n=2, n=3, n=4,$ and $n=5.$ $a_1 = \frac{(-1)^{(1-1)} }{5^1}=\frac{1}{5}$ $a_2 = \frac{(-1)^{(2-1)} }{5^2}=-\frac{1}{25}$ $a_3 = \frac{(-1)^{(3-1)} }{5^3}=\frac{1}{125}$ $a_4 = \frac{(-1)^{(4-1)} }{5^4}=-\frac{1}{625}$ $a_5 = \frac{(-1)^{(5-1)} }{5^5}=\frac{1}{3125}$ Hence we see that the first five terms are $\frac{1}{5},-\frac{1}{25},\frac{1}{125},-\frac{1}{625}, \frac{1}{3125}$
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