University Calculus: Early Transcendentals (3rd Edition)

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 - Exercises - Page 549: 7



Work Step by Step

Formula to find the binomial series is: $(1+x)^m=1+\Sigma_{k=1}^\infty \dbinom{m}{k}x^k$ Here, $\dbinom{m}{k}=\dfrac{m(m-1)(m-2).....(m-k+1)}{k!}$ Now, $(1+x^3)^{-1/2}=1-\dfrac{1}{2}(x^3)+\dfrac{(\dfrac{-1}{2})(-\dfrac{3}{2})(x^3)}{2!}+\dfrac{(-\dfrac{1}{2})(-\dfrac{3}{2})(-\dfrac{5}{2})(x^3)}{3!}+...$ Thus, the first four terms are: $1-\dfrac{1}{2}x^3+\dfrac{3}{8}x^6-\dfrac{5}{16}x^9+...$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.