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Prove that the series obtained in Exercise 18 represents $ \cosh 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

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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.

01:30

Prove that the series obta…

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The problem is proof that of serious about finding exercise. A team represents cortex or axe. So after works is they go to coach thanks, which is equal to two acts. Us it connective ax over too. So you're absolutely or fax his last twenty half coach Axe this last time, too. Andi think shacks. It's also last time you should be on behalf and the derivative off half a box. ISS last, too. On behalf Arup Bond Our axe as value off our necks this last time need to the hams absolutely off X to the power ofthe past one over and plus one bacterial. This is the limit and cost to infinity into the Tom's Ex two plus one over plus Long Factory alone. It's equal to zero for all acts on behalf Limit on God's three affinity. I'm equal to zero to the Siri's off time to exercise eighteen represents coach acts for all axe

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