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: 11



Work Step by Step

The formula to determine the binomial series is: $(1+x)^p=1+\Sigma_{k=1}^\infty \dbinom{p}{k}x^k$ Here, $\dbinom{p}{k}=\dfrac{p(p-1)(p-2).....(p-k+1)}{k!}$ Now, $(1+x)^{4}=1+4x+\dfrac{(4)(3)x^2}{2!}+\dfrac{(4)(3)(2)x^3}{3!}+\dfrac{(4)(3)(2)(1)x^4}{4!}...$ Thus, the first four terms are: $1+4x+6x^2+4x^3+x^4$
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