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Find the Maclaurin series for the functions.$$\sin \frac{x}{2}$$

$$\frac{x}{2}-\frac{x^{3}}{2^{3} \cdot 3 !}+\frac{x^{5}}{2^{5} \cdot 5 !}-\dots$$

Calculus 2 / BC

Chapter 10

Infinite Sequences and Series

Section 8

Taylor and Maclaurin Series

Series

Campbell University

Oregon State University

University of Michigan - Ann Arbor

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.

00:39

Find the Maclaurin series …

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04:09

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01:02

For the ma chlorin series of the function sine x over 2, we use the result to mac. Clarin'S series of sine of x is equal to sum, and from 0 to infinity negative 1 to the power of n x to the power 2 n plus 1. Over 2 n plus 1 factorial, then we place x by x over 2 behalf in the color in series of the function sine x. Over 2 is equal to some and from 0 to infinity negative 12 n times x, 22 n plus 1 over 2 to the power 2 plus 1 multiply 2 n plus 1 factorial.

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