Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 10: Infinite Sequences and Series - Section 10.10 - The Binomial Series and Applications of Taylor Series - Exercises 10.10 - Page 633: 13



Work Step by Step

Apply the binomial series formula to determine the first four terms: $(1+x)^r=1+\Sigma_{k=1}^\infty \dbinom{r}{k}x^k$ Here, we have $\dbinom{r}{k}=\dfrac{r(r-1)(r-2).....(r-k+1)}{k!}$ Now, we have $(1-2x)^{3}=1+3(-2x)+\dfrac{(3)(2)}{2!}(4x^2)+\dfrac{(3)(2)(1)}{3!}(-8)x^3=1-6x+12x^2-8x^3$
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