Answer
$\dfrac{5}{3}$
Work Step by Step
Here, $a=1, r=\dfrac{2}{5}$; The common ratio is $|\dfrac{2}{5}| \lt 1$; so the series converges.
The sum of a geometric series can be found as:
$S=\dfrac{a}{1-r}=\dfrac{1}{1-\dfrac{2}{5}}=\dfrac{5}{3}$
University Calculus: Early Transcendentals (3rd Edition)
by Hass, Joel R.; Weir, Maurice D.; Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0321999584
ISBN 13:
978-0-32199-958-0
Chapter 9 - Section 9.2 - Infinite Series - Exercises - Page 497: 15
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