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Use the definition of a Taylor series to find the first four nonzero terms of the series for $ f(x) $ centered at the given value of $ a. $

$ f(x) = \ln x, $ $ a = 1 $

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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

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.

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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Use the definition of a Ta…

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a. Use the definition of a…

The problem is, use the definition of Attila Siri's to find a first born and zero terms off the Siri's. For relax. Centered is a given volume off. Hey, so first you have one day, see what zero I've X from. Say what? One over max. So half problem on one issue. One second derivative secret Addictive one over X squire. So have crumb crumb at point one zero two to one. Asked crime from prom as they called you to our backs. Q. So, prom, prom, prom one acts because it's a good one. This is equal to true in the first four Nancy with terms of Siri's. Relax when also need Thio Compute most decorative, cystic or too active truth towns. Three. Over Act two. Four. So a fruit fourth directive is appoint one. It's called connecting six. Then the first born and zero terms of the Siri's or relax centered cut one. Dennis precipitously one over one times X. Second, this is ninety one over to factorial exclaim his X minus one next month. One squire, us two over should have three x minus Wass Cube. Ask ninety six over two times three counts for excellence. One to the public for so this's equal to X minus one US LINUS one over two x minus one Squire plus one over three X months one cube minus one War X minus one through four This other first two four nine zero terms.

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