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 10.8 - Taylor and Maclaurin Series - Exercises 10.8 - Page 618: 12

Answer

$\Sigma_{n=0}^\infty\dfrac{x^{n+1}}{n!}$

Work Step by Step

Consider the Maclaurin Series for $e^x$ as follows: $e^x=\Sigma_{n=0}^\infty (\dfrac{x^n}{n!})$ Multiply the above series with $x$ we get $xe^x=\Sigma_{n=0}^\infty \dfrac{x \cdot x^n}{n!}=\Sigma_{n=0}^\infty\dfrac{x^{n+1}}{n!}$
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