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Use the result of Example 7 to compute $ \arctan 0.2 $ correct to five decimal places.

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Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 9

Representations of Functions as Power Series

Sequences

Series

Campbell University

Harvey Mudd College

Baylor University

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.

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Use the result of Example …

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Use a calculator to approx…

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the problem is, use a result of the example sermon to compute attendant to steer a point to correct too fast decimal places. You exercised someone we have Our attendant axe is they got to some from zero to twenty makes you want to pop off and terms axe to the off, too, and plus Juan over to him. Asked what things? Zero point two to the power of nine. This is the country father onto one, too. Ham's tend to the part ofthe negative someone, so we're half hand. They want to is about zero point. Shoo Hu Wan minus zero point two to the power of three over three. Thus zero point two to the power off half over far minus zero point two to the power of seven off sullen, which is about zero point one nine seven or zero.

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