Answer
$\dfrac{4}{5}$
Work Step by Step
Since, we have the form of the given series as: $\dfrac{1}{1+x}=1-x+x^2-x^3+....+(-x)^n$
Here, $x=\dfrac{1}{4}$
Thus, the sum of the series is:
$\dfrac{1}{1+\dfrac{1}{4}}=\dfrac{4}{4+1}=\dfrac{4}{5}$
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 9.10 - The Binomial Series and Applications of Taylor Series - Practice Exercises - Page 553: 51
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