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: 3



Work Step by Step

Apply Binomial series formula to find the first four terms. $(1+x)^m=1+\Sigma_{k=1}^\infty \dbinom{m}{k}x^k$ and $\dbinom{m}{k}=\dfrac{m(m-1)(m-2).....(m-k+1)}{k!}$ Thus,$(1-x)^{-3}=1+(-3)(-x)+\dfrac{(-3)(-4)(-x^2)}{2!}+\dfrac{(-3)(-4)(-5)(-x^3)}{3!}+...=1+3x+6x^2+10x^3+...$ Hence, we have the first four terms are: $1+3x+6x^2+10x^3$
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