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Find a power series representation for the function and determine the radius of convergence.$ f(x) = \frac {x^2 + x}{(1 - x)^3} $

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Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 9

Representations of Functions as Power Series

Sequences

Series

Oregon State University

Baylor University

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.

05:30

Find a power series repres…

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please. Yeah. Okay. So find the power serious reputation for the function and determine the raiders Convergence. So at that sequels X squared plus x times, the sea jets and Drea s equals one or women's X cube. And we got first expand GS and the expanding equals two from zero to infinity. That CDO the infamous extra power vent and the equations by the binomial theorem is going to be one plus three minus in class three, minus one or over and minus one. No, this over in. Yes. So this is going to be in from zero to infinity and plus two who is in Tom's asked to power in and we plug in Jack's into the equation one. So the fundraise off after Pat's he's going to be and, hey, signal from zero to infinity. And that's to choose in extra power and plus two class and from zero to infinity, the interest to over in absolute heart and plus one and the readers convergence is gonna be Are you close? One

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