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Prove that the series obtained in Exercise 13 represents $ \cos 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
Baylor University
University of Michigan - Ann Arbor
Boston College
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.
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Prove that the series obta…
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In Exercises $13-16,$ prov…
The problem is proof that Siri's of changing exercise thirteen represents co sign Axe for or Axe in exercise. Thirteen. We're half So my Clarence theories focus on tax. This sum from zero to infinity. Nick, do you want to end hams? Axe to two and over two in Factorial so we can say this is on alternating Siri's. So the art imitating Siri's estimation theory, um shows as Eric involved in this approx approximation our two and x this last time axe too. Shoot. Perhaps I'm plus one over to M plus one Factorial. Yeah, you have squalor you smaller than this one. And this thing is the limit on goes to infinity access to M plus two over two and plus two bacterial secret zero. It's over half lim our two and my hand cost to infinity is equal to zero so that there is a change in exercise. Thirteen. This Siri's represents Kasan axe or axe
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