Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 11 - Infinite Sequences and Series - Problems Plus - Problems - Page 827: 1


$$\frac{15!}{5!}=6\times 7\times 8........\times 15$$

Work Step by Step

Write the Taylor's series for$sinx=x-\frac{1}{3!}x^3+\frac{1}{5!}x^5-.....$ For $f^{15}(x)=sinx^3=x^3-\frac{1}{3!}x^9+\frac{1}{5!}x^15-.....$ Now, $f^{15}(0)=sin(x^{3})^{15}(0)=\frac{15!}{5!}$ The required result is: $$\frac{15!}{5!}=6\times 7\times 8........\times 15$$
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