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Express the function as the sum of a power series by first using partial fractions. Find the interval of convergence.$ f(x) = \frac {2x + 3}{x^2 + 3x + 2} $

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Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 9

Representations of Functions as Power Series

Sequences

Series

University of Michigan - Ann Arbor

University of Nottingham

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.

04:10

Express the function as th…

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02:38

04:50

09:44

$11-12$ Express the functi…

03:25

02:47

02:22

13:23

12:47

02:15

01:18

Find a power series repres…

02:11

01:39

okay. So expressive function as a sum of power, serious by first using partial fractions and find the in the role of convergence. So that bag's equals to ask for three times. So we're going to fetter out this part, It becomes at plus one times. This was too one over it. And this is just so it's a difference of two factions when investment plus one minus one or restless too. Yeah, and, ah, we can expand this part from that firm. And it just not wanted power in extra power and from zero to infinity minus. So actually, we're here. We're gonna hold out to here. So becomes one of us. Have bags end. This is just what happy soul here, minus one two hour in extra oven, over to help it. And from zero to infinity. I know him. I might as well just But it's who inside it. So this is to empower us one, and yeah, this is help. Our serious and Phil can simplify it. Bye. Plus tax insurance, the's some, but okay, we can wield it as an alternative form. So this is the same one. But if you want to know that we can destroy it. Extroverted plus one minus. If you're dating like you want our end acts to power. Plus one answered about this one. So this is the to ask past this part which is right here a parenthesis here. And the three comes this part. Here, have this that you want a part in that of an over tubes of this one. Done and find the interval burdens so we can fund it from here. Think, Creon one. So s the absolutely fattest, less than one end two over axe. That's over to the absolutely the absolute Oh, that's over, too. Is less than one wishing kleiss the interval convergence I because a two one, two, one. Okay.

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