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Prove that the series obtained in Exercise 25 represents $ \sin x $ for all $ x. $

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Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 10

Taylor and Maclaurin Series

Sequences

Series

Campbell University

Oregon State University

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.

02:28

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. Formally, a sequence can be defined as a function whose domain is either the set of the natural numbers (for infinite sequences) or the set of the first "n" natural numbers (for a finite sequence). A sequence can be thought of as a list of elements with a particular order. Sequences are useful in a number of mathematical disciplines for studying functions, spaces, and other mathematical structures using the convergence properties of sequences. In particular, sequences are the basis for series, which are important in differential equations and analysis. Sequences are also of interest in their own right and can be studied as patterns or puzzles, such as in the study of prime numbers.

06:11

Prove that the series obta…

01:35

11:31

02:09

06:19

01:30

The problem is proof that if Siri's of finding exercise on Your staff represents sign acts for all acts, so first in exercise on the farm we have Siri's is some on from zero to infinity makes you want to the part of plus one times X minus pi two, two and one over two and plus one factorial so we can see this is on alternating Siri's. So they are donating Siri's estimation. Siri, um, show that error involved in this approximation. Our shoe and last one Thanks absolutely with this one is last X minus pi Absolute value shuen plus three over shuen plus three factorial the's the limit and goes to infinity Xmas pie to end Class three offer it to M plus three. Bacterial is equal to zero for honey Max, it's over half limit, uh, shoe and plus one. What endorsing twenties? Got zero max. Then we have the theories. Siri's represents sign axe for all Axe

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