Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 11 - Infinite Series - 11.7 Taylor Series - Exercises - Page 589: 66



Work Step by Step

Since we have$$ 1-4 x+4^{2} x^{2}-4^{3} x^{3}+4^{4} x^{4}-4^{5} x^{5}+\cdots\\ =1-4 x+(4 x)^{2}-(4 x)^{3}+(4 x)^{4}-(4 x)^{5}+\cdots $$ Then by using Table 2, we see that this is Maclaurin series of the function $$\frac{1}{1+4x}.$$
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