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Find the Maclaurin series for the functions$$X e^{x^{x}}$$

$$x e^{x}=\sum_{n=0}^{\infty} \frac{x^{n+1}}{n !}$$

Calculus 2 / BC

Chapter 10

Infinite Sequences and Series

Section 8

Taylor and Maclaurin Series

Series

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Lectures

01:59

In mathematics, a series is, informally speaking, the sum of the terms of an infinite sequence. The sum of a finite sequence of real numbers is called a finite series. The sum of an infinite sequence of real numbers may or may not have a well-defined sum, and may or may not be equal to the limit of the sequence, if it exists. The study of the sums of infinite sequences is a major area in mathematics known as analysis.

14:11

In mathematics, the partial sums of a series are the sums of all terms of the series except possibly the first and last.

01:17

Find the Maclaurin series …

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For the mac chlorine series of function x times e to x, so first mac chloris series of each is x, is 1 plus x, plus x, squared over 2 factorium plus x cubed over 3 factorial plus to do which is equal to sum and from 0 to Infinity x to the power n over n factorial, here we assume 0 factorial is equal to 1. Then mac claren's series of the function x times e to x is equal to x times sum and from 0 to infinity x, 2 n over n factorial, which is equal to sam and from 0 to infinity, x, 2 n plus 1 over n factorial.

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