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Prove that the series obtained in Exercise 17 represents $ \sinh 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

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

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.

02:02

Prove that the series obta…

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02:04

The problem is proof that if Siri's obtained in Exercise seventeen represents St Acts, all acts first. Though we have our backs, it's called a cinch axe, which is? They just tow X minus two connected backs over to one absolute value ofthe axe is last. Behalf Finch Axe After a while, your syntax is last time, you think. And that's why you off coach Checks is also asked me to be on behalf and derivative off It works. How swallows this one last thing on behalf our necks absolutely off Max this last time, too. Holmes, absolutely off axed and plus one over it. And plus one Torrio since the limit and goes to vanity into the hams. Packs two plus one over and plus one factory alone. Yes, equal to zero for our axe. Half the limit. Our necks. What costume Serenity is four to zero, so we have the Siri's obtained in exercise. Seventeen represents cinch axe off all axe

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