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Use the binomial series to expand the function as a power series. State the radius of convergence.

$ \frac {1}{(2 + x)^3} $

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Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 10

Taylor and Maclaurin Series

Sequences

Series

Missouri State University

Baylor University

Idaho State University

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.

02:06

Use the binomial series to…

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the problem is use about nominal Siri's to expand the function as a power. Siri's stated the readers of Emergence one over two plus snacks to the Final Three. The fruit is to become rewriting this function. Two two negative three pounds. One of us affects older two to the power of ninety three, the best forming over how this is going to to times two to the power of negative three. Hans Song from zero to Infinity. Is this this negative? Three. Yeah, I'm just over two users to the public. This's equal the song from serial between Trinity Green over to US. Three count snacks, too. I'm a computer. The limit on a cost. Three. Infinity negative three plus one over to the war arms should to come past green off the invective. Three. This is the limit and cost serenity. Negative. Three. Wireless on. I want you over truth hams and plus one. So this is a good one half. So the readers of convergence it's legal to true

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