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

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$\sum_{n=0}^{\infty}(2 n+1) x^{n}, \quad R=1$

Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 9

Representations of Functions as Power Series

Sequences

Series

Oregon State University

Harvey Mudd College

Idaho State University

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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Find a power series repres…

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Find a power-series repres…

find the power serious representation of a function and determine the readers of burdens. So after facts, because one person likes times the derivative of one over one minus X in terms that one. So let's see if it's crept. So one hour was X and everything is gonna be when you work. One one is just my woman's X square and like one here. So you have filtered into one. So this is true, okay? And we continue. We can expand this part so it becomes minus one minus X guns, sir. Zero from any from zero to infinity. An expert in And is it just knight to not to go from zero to open day expelled in minus stew and from zero to in any hour end class work and the fun the reserve burdens it requires absolute. That is less than one. Which place are equals. What? Okay,

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