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Find a power series representation for the function and determine the interval of convergence.$ f(x) = {x + a}{x^2 + a^2}, a > 0 $

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$\left(x^{0}, 1, a\right)$

Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 9

Representations of Functions as Power Series

Sequences

Series

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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.

02:21

Find a power series repres…

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02:53

so fun houses the reputation for the function FX and determine the in the role of convergence. So if x equals, it's worth us experts eight times expire and Ace is a positive number. So this is our way of power. Siri's. So this is a polynomial, and we fund that it has. So the coefficient of X to the power zero is a square And that sit that of the ex term, this one and that if the Expressionists eh? And so awful Intermix zero zero zero zero zero. So that is our area power Siri's. So this is thie code revisions. That's her so efficient that way yet So it's a royal power. Siri's on determine the winner will pin murders on DSO FX. We'LL always converge to itself. So we're going to see the honorable two murders. Is thie whole real lion. So is out of the room number

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