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: 12



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 $(1+x^2)^{3}=1+3x^2+\dfrac{(3)(2)}{2!}(x^2)^2+\dfrac{(3)(2)(1)}{3!}(x^2)^3+0$ Hence, our first four terms are: $1+3x^2+3x^4+x^6$
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.