College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 8, Sequences and Series - Section 8.6 - The Binomial Theorem - 8.6 Exercises: 32

Answer

The first 3 terms are: $x^{40}$ $40x^{38}$ $780x^{36}$

Work Step by Step

We find the first 3 terms in the expansion of $(x+ \frac{1}{x})^{40}$ by using Binomial Theorem coefficients: $\left(\begin{array}{l} 40\\ 0\end{array}\right)x^{40}(\frac{1}{x})^0=x^{40}$ $\left(\begin{array}{l} 40\\ 1 \end{array}\right)x^{39}(\frac{1}{x})^1=40x^{38}$ $\left(\begin{array}{l} 40\\ 2 \end{array}\right)x^{38}(\frac{1}{x})^{2}=780x^{36}$
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