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Find the first three nonzero terms of the Maclaurin series for each function and the values of $x$ for which the series converges absolutely.$$f(x)=(\sin x) \ln (1+x)$$

$$f(x)=\sin x \cdot \ln (1+x) \text { is } x^{2}-\frac{x^{3}}{2}+\frac{x^{4}}{6}-\cdots$$

Calculus 2 / BC

Chapter 10

Infinite Sequences and Series

Section 8

Taylor and Maclaurin Series

Series

Missouri State University

Harvey Mudd College

Idaho State University

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.

03:35

Find the first three nonze…

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